gdz.top
Номер 130, страница 236 - гдз по физике 10-11 класс задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Задачник
Издательство: Илекса
Год издания: 2008 - 2026
Уровень обучения: профильный
Цвет обложки: красный лупа, парень едет на велосипеде
ISBN: 978-5-89237-252-7
Популярные ГДЗ в 10 классе
Электродинамика. Магнитное поле. 32. Электромагнитная индукция. Олимпиадные задачи - номер 130, страница 236.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319775 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-130" "field_display_title" => "130" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:2 [ 0 => App\Models\Term {#1044 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" …26 } 1 => App\Models\Term {#1045 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:3 [ 0 => App\Models\Term {#1049 …30} 1 => App\Models\Term {#1050 …30} 2 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 …30} ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 …30} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "163" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:4 [ 0 => App\Models\Branch {#1120 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Book {#1122 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Term {#1123 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:2 [ 0 => App\Models\Term {#1126 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:3 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:1 [ 0 => App\Models\Term {#1136 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Term {#1138 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Term {#1140 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Term {#1144 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #original: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1151 #items: array:1 [ 0 => App\Models\Term {#1152 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #original: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1124} "field_class" => Illuminate\Database\Eloquent\Collection {#1125} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128} "field_author" => Illuminate\Database\Eloquent\Collection {#1130} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1134} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_country" => Illuminate\Database\Eloquent\Collection {#1137} "field_city" => Illuminate\Database\Eloquent\Collection {#1139} "field_series" => Illuminate\Database\Eloquent\Collection {#1141} "field_umk" => Illuminate\Database\Eloquent\Collection {#1142} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1143} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1148} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1149} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1150} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1151} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "163" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1155} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1154 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319364 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Магнитное поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "220" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319364 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Магнитное поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1156} "field_page_start" => "220" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1157} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1159 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319368 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "32. Электромагнитная индукция" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "230" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:1 [ 0 => App\Models\Branch {#1169 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319364 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Магнитное поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1171 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "220" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319364 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Магнитное поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1171} "field_page_start" => "220" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1172} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1173} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319368 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "32. Электромагнитная индукция" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1160} "field_page_start" => "230" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1161} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1170} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Branch {#1163 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319370 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1162 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "236" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1166 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1179 #items: array:1 [ 0 => App\Models\Branch {#1178 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319368 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "32. Электромагнитная индукция" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1180 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "230" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1182 #items: array:1 [ 0 => App\Models\Branch {#1169} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319368 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "32. Электромагнитная индукция" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1180} "field_page_start" => "230" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1181} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1182} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319370 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1162} "field_page_start" => "236" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1166} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1179} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:2 [ 0 => App\Models\Element {#1101 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1494108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1100 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\Term {#1099 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319775" "type" => "task" ] "text" => "<p><strong>O30.</strong> Виток изолированного провода изогнут в виде восьмерки (см. рисунок), так что $r_1 = 20$ мм и $r_2 = 60$ мм. В течение промежутка времени $\Delta t = 0,50$ мс однородное магнитное поле, перпендикулярное плоскости витка, равномерно возрастает от нуля до $B = 5$ Тл. На какое напряжение $\text{U}$ должна быть рассчитана изоляция между проводами, чтобы не произошел ее пробой?</p><p>☑ U > 38$ В.</p><p><strong><em>Решение.</em></strong> Обозначим сопротивления верхнего и нижнего колец «восьмерки» соответственно $R_1$ и $R_2$, а индуцируемые в них ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$. Эти ЭДС действуют в цепи навстречу друг другу. Пробой возможен между точками $\text{A}$ и $\text{B}$ на перемычке «восьмерки» (см. эквивалентную схему цепи на рисунке).</p><p><strong>Согласно закону Ома</strong></p><p>$I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 + R_2}$, $U_{AB} = \mathcal{E}_2 - I R_2 = \frac{\mathcal{E}_2 R_1 + \mathcal{E}_1 R_2}{R_1 + R_2}$.</p><p>Используя закон электромагнитной индукции и учитывая, что $R_2/R_1 = r_2/r_1$, получаем $U_{AB} = \pi B r_1 r_2 / \Delta t = 38$ (В).</p><p>О31. Катушка имеет индуктивность $\text{L}$ и электрическое сопро-</p>" "img" => array:1 [ 0 => array:5 [ "name" => "130-1.jpg" "alt" => null "width" => "1396" "height" => 1529 "path" => "/media/fizika_10/gelfgat-z/0-olimp/130-1.webp?ts=1756251279" ] ] ] #original: array:7 [ "id" => 1494108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1319775" "type" => "task" ] "text" => "<p><strong>O30.</strong> Виток изолированного провода изогнут в виде восьмерки (см. рисунок), так что $r_1 = 20$ мм и $r_2 = 60$ мм. В течение промежутка времени $\Delta t = 0,50$ мс однородное магнитное поле, перпендикулярное плоскости витка, равномерно возрастает от нуля до $B = 5$ Тл. На какое напряжение $\text{U}$ должна быть рассчитана изоляция между проводами, чтобы не произошел ее пробой?</p><p>☑ U > 38$ В.</p><p><strong><em>Решение.</em></strong> Обозначим сопротивления верхнего и нижнего колец «восьмерки» соответственно $R_1$ и $R_2$, а индуцируемые в них ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$. Эти ЭДС действуют в цепи навстречу друг другу. Пробой возможен между точками $\text{A}$ и $\text{B}$ на перемычке «восьмерки» (см. эквивалентную схему цепи на рисунке).</p><p><strong>Согласно закону Ома</strong></p><p>$I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 + R_2}$, $U_{AB} = \mathcal{E}_2 - I R_2 = \frac{\mathcal{E}_2 R_1 + \mathcal{E}_1 R_2}{R_1 + R_2}$.</p><p>Используя закон электромагнитной индукции и учитывая, что $R_2/R_1 = r_2/r_1$, получаем $U_{AB} = \pi B r_1 r_2 / \Delta t = 38$ (В).</p><p>О31. Катушка имеет индуктивность $\text{L}$ и электрическое сопро-</p>" "img" => array:1 [ 0 => array:5 [ "name" => "130-1.jpg" "alt" => null "width" => "1396" "height" => 1529 "path" => "/media/fizika_10/gelfgat-z/0-olimp/130-1.webp?ts=1756251279" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1093 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1691665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Edition {#1094 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1092 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319775" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Радиус меньшего кольца, $r_1 = 20 \text{ мм}$<br>Радиус большего кольца, $r_2 = 60 \text{ мм}$<br>Промежуток времени, $\Delta t = 0.50 \text{ мс}$<br>Начальная индукция магнитного поля, $B_0 = 0 \text{ Тл}$<br>Конечная индукция магнитного поля, $B = 5 \text{ Тл}$<br></p><p>Перевод в систему СИ:<br>$r_1 = 20 \times 10^{-3} \text{ м} = 0.02 \text{ м}$<br>$r_2 = 60 \times 10^{-3} \text{ м} = 0.06 \text{ м}$<br>$\Delta t = 0.50 \times 10^{-3} \text{ с}$<br>Изменение магнитной индукции, $\Delta B = B - B_0 = 5 \text{ Тл}$</p><p><strong>Найти:</strong></p><p>Минимальное напряжение $U$, на которое должна быть рассчитана изоляция.</p><p><strong>Решение:</strong></p><p>При изменении магнитного потока $\Phi$ через замкнутый контур в нем возникает ЭДС индукции $\mathcal{E}$, величина которой определяется законом электромагнитной индукции Фарадея:</p><p>$|\mathcal{E}| = \left|-\frac{\Delta \Phi}{\Delta t}\right|$</p><p>Магнитный поток через площадку $S$ в однородном магнитном поле, перпендикулярном этой площадке, равен $\Phi = B \cdot S$. Поскольку магнитное поле нарастает равномерно, скорость его изменения постоянна. Тогда ЭДС индукции в контуре можно рассчитать как:</p><p>$|\mathcal{E}| = S \cdot \frac{\Delta B}{\Delta t}$</p><p>Виток в форме "восьмерки" состоит из двух колец, площади которых $S_1 = \pi r_1^2$ и $S_2 = \pi r_2^2$. Так как провод обходит эти кольца в противоположных направлениях (например, одно по часовой стрелке, а другое — против), то согласно правилу Ленца, индуцируемые в них ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$ будут направлены навстречу друг другу. Электрическая схема такого витка эквивалентна двум источникам ЭДС, соединенным встречно.</p><p>ЭДС, индуцируемые в каждом кольце, равны:</p><p>$\mathcal{E}_1 = S_1 \frac{\Delta B}{\Delta t} = \pi r_1^2 \frac{\Delta B}{\Delta t}$</p><p>$\mathcal{E}_2 = S_2 \frac{\Delta B}{\Delta t} = \pi r_2^2 \frac{\Delta B}{\Delta t}$</p><p>Наибольшая разность потенциалов, которая может привести к пробою изоляции, возникает в точке пересечения провода. В эквивалентной схеме это напряжение $U$ на зажимах между двумя источниками. Сопротивления участков провода, образующих кольца ($R_1$ и $R_2$), пропорциональны их длинам, то есть $R \sim L = 2\pi r$. Следовательно, отношение сопротивлений равно отношению радиусов:</p><p>$\frac{R_1}{R_2} = \frac{r_1}{r_2}$</p><p>Для схемы из двух встречно соединенных источников с ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$ и внутренними сопротивлениями $R_1$ и $R_2$, напряжение на зажимах $U$ определяется по формуле:</p><p>$U = \frac{\mathcal{E}_1 R_2 + \mathcal{E}_2 R_1}{R_1 + R_2}$</p><p>Подставим в эту формулу выражения для ЭДС и соотношение сопротивлений:</p><p>$U = \frac{(\pi r_1^2 \frac{\Delta B}{\Delta t}) R_2 + (\pi r_2^2 \frac{\Delta B}{\Delta t}) R_1}{R_1 + R_2}$</p><p>Вынесем общие множители и разделим числитель и знаменатель на $R_2$:</p><p>$U = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 R_2 + r_2^2 R_1}{R_1 + R_2} = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_2^2 (R_1/R_2)}{(R_1/R_2) + 1}$</p><p>Подставим $\frac{R_1}{R_2} = \frac{r_1}{r_2}$:</p><p>$U = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_2^2 (r_1/r_2)}{(r_1/r_2) + 1} = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_1 r_2}{(r_1+r_2)/r_2} = \pi \frac{\Delta B}{\Delta t} \frac{r_1(r_1 + r_2)r_2}{r_1+r_2}$</p><p>После сокращения получаем простую формулу:</p><p>$U = \pi r_1 r_2 \frac{\Delta B}{\Delta t}$</p><p>Подставим числовые значения из условия задачи в систему СИ:</p><p>$U = \pi \cdot (0.02 \text{ м}) \cdot (0.06 \text{ м}) \cdot \frac{5 \text{ Тл}}{0.50 \times 10^{-3} \text{ с}}$</p><p>$U = \pi \cdot 0.0012 \cdot 10^4 = 12\pi \text{ В}$</p><p>Вычислим приближенное значение, используя $\pi \approx 3.14159$:</p><p>$U \approx 12 \cdot 3.14159 \approx 37.7 \text{ В}$</p><p>Округляя результат до двух значащих цифр, получаем 38 В. Это означает, что изоляция должна быть рассчитана на напряжение не менее 38 В, чтобы избежать электрического пробоя.</p><p><strong>Ответ:</strong> Изоляция должна быть рассчитана на напряжение $U \ge 38 \text{ В}$.</p>" ] #original: array:6 [ "id" => 1691665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085} "task" => array:2 [ "refs" => "1319775" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Радиус меньшего кольца, $r_1 = 20 \text{ мм}$<br>Радиус большего кольца, $r_2 = 60 \text{ мм}$<br>Промежуток времени, $\Delta t = 0.50 \text{ мс}$<br>Начальная индукция магнитного поля, $B_0 = 0 \text{ Тл}$<br>Конечная индукция магнитного поля, $B = 5 \text{ Тл}$<br></p><p>Перевод в систему СИ:<br>$r_1 = 20 \times 10^{-3} \text{ м} = 0.02 \text{ м}$<br>$r_2 = 60 \times 10^{-3} \text{ м} = 0.06 \text{ м}$<br>$\Delta t = 0.50 \times 10^{-3} \text{ с}$<br>Изменение магнитной индукции, $\Delta B = B - B_0 = 5 \text{ Тл}$</p><p><strong>Найти:</strong></p><p>Минимальное напряжение $U$, на которое должна быть рассчитана изоляция.</p><p><strong>Решение:</strong></p><p>При изменении магнитного потока $\Phi$ через замкнутый контур в нем возникает ЭДС индукции $\mathcal{E}$, величина которой определяется законом электромагнитной индукции Фарадея:</p><p>$|\mathcal{E}| = \left|-\frac{\Delta \Phi}{\Delta t}\right|$</p><p>Магнитный поток через площадку $S$ в однородном магнитном поле, перпендикулярном этой площадке, равен $\Phi = B \cdot S$. Поскольку магнитное поле нарастает равномерно, скорость его изменения постоянна. Тогда ЭДС индукции в контуре можно рассчитать как:</p><p>$|\mathcal{E}| = S \cdot \frac{\Delta B}{\Delta t}$</p><p>Виток в форме "восьмерки" состоит из двух колец, площади которых $S_1 = \pi r_1^2$ и $S_2 = \pi r_2^2$. Так как провод обходит эти кольца в противоположных направлениях (например, одно по часовой стрелке, а другое — против), то согласно правилу Ленца, индуцируемые в них ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$ будут направлены навстречу друг другу. Электрическая схема такого витка эквивалентна двум источникам ЭДС, соединенным встречно.</p><p>ЭДС, индуцируемые в каждом кольце, равны:</p><p>$\mathcal{E}_1 = S_1 \frac{\Delta B}{\Delta t} = \pi r_1^2 \frac{\Delta B}{\Delta t}$</p><p>$\mathcal{E}_2 = S_2 \frac{\Delta B}{\Delta t} = \pi r_2^2 \frac{\Delta B}{\Delta t}$</p><p>Наибольшая разность потенциалов, которая может привести к пробою изоляции, возникает в точке пересечения провода. В эквивалентной схеме это напряжение $U$ на зажимах между двумя источниками. Сопротивления участков провода, образующих кольца ($R_1$ и $R_2$), пропорциональны их длинам, то есть $R \sim L = 2\pi r$. Следовательно, отношение сопротивлений равно отношению радиусов:</p><p>$\frac{R_1}{R_2} = \frac{r_1}{r_2}$</p><p>Для схемы из двух встречно соединенных источников с ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$ и внутренними сопротивлениями $R_1$ и $R_2$, напряжение на зажимах $U$ определяется по формуле:</p><p>$U = \frac{\mathcal{E}_1 R_2 + \mathcal{E}_2 R_1}{R_1 + R_2}$</p><p>Подставим в эту формулу выражения для ЭДС и соотношение сопротивлений:</p><p>$U = \frac{(\pi r_1^2 \frac{\Delta B}{\Delta t}) R_2 + (\pi r_2^2 \frac{\Delta B}{\Delta t}) R_1}{R_1 + R_2}$</p><p>Вынесем общие множители и разделим числитель и знаменатель на $R_2$:</p><p>$U = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 R_2 + r_2^2 R_1}{R_1 + R_2} = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_2^2 (R_1/R_2)}{(R_1/R_2) + 1}$</p><p>Подставим $\frac{R_1}{R_2} = \frac{r_1}{r_2}$:</p><p>$U = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_2^2 (r_1/r_2)}{(r_1/r_2) + 1} = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_1 r_2}{(r_1+r_2)/r_2} = \pi \frac{\Delta B}{\Delta t} \frac{r_1(r_1 + r_2)r_2}{r_1+r_2}$</p><p>После сокращения получаем простую формулу:</p><p>$U = \pi r_1 r_2 \frac{\Delta B}{\Delta t}$</p><p>Подставим числовые значения из условия задачи в систему СИ:</p><p>$U = \pi \cdot (0.02 \text{ м}) \cdot (0.06 \text{ м}) \cdot \frac{5 \text{ Тл}}{0.50 \times 10^{-3} \text{ с}}$</p><p>$U = \pi \cdot 0.0012 \cdot 10^4 = 12\pi \text{ В}$</p><p>Вычислим приближенное значение, используя $\pi \approx 3.14159$:</p><p>$U \approx 12 \cdot 3.14159 \approx 37.7 \text{ В}$</p><p>Округляя результат до двух значащих цифр, получаем 38 В. Это означает, что изоляция должна быть рассчитана на напряжение не менее 38 В, чтобы избежать электрического пробоя.</p><p><strong>Ответ:</strong> Изоляция должна быть рассчитана на напряжение $U \ge 38 \text{ В}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319776" "type" => "task" ] "previous" => array:2 [ "refs" => "1319774" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\BookPage {#1106 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1341197 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-236" "field_display_title" => "236" "field_folder" => "1" "field_image_name" => "236" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Element {#1108 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1519742 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Edition {#1100} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "236-1.jpg" "alt" => null "width" => "1577" "height" => 2447 "path" => "/media/fizika_10/gelfgat-z/0-1/236-1.webp?ts=1756642404" ] ] ] #original: array:6 [ "id" => 1519742 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115} "book_page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "236-1.jpg" "alt" => null "width" => "1577" "height" => 2447 "path" => "/media/fizika_10/gelfgat-z/0-1/236-1.webp?ts=1756642404" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1341198" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341196" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:2 [ 0 => App\Models\Task {#1289 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319775 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-130" "field_display_title" => "130" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1291 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ 0 => App\Models\Branch {#1120} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 #items: array:4 [ 0 => App\Models\Branch {#1120} 1 => App\Models\Branch {#1154} 2 => App\Models\Branch {#1159} 3 => App\Models\Branch {#1163} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:2 [ 0 => App\Models\Element {#1101} 1 => App\Models\Element {#1093} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319776" "type" => "task" ] "previous" => array:2 [ "refs" => "1319774" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1295 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319775 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-130" "field_display_title" => "130" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1291} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1292} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293} "content" => Illuminate\Database\Eloquent\Collection {#1294} "next" => array:2 [ "refs" => "1319776" "type" => "task" ] "previous" => array:2 [ "refs" => "1319774" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1295} "page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1296 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319776 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_page_end" => "237" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-131" "field_display_title" => "131" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1298 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:1 [ 0 => App\Models\Branch {#1120} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:4 [ 0 => App\Models\Branch {#1120} 1 => App\Models\Branch {#1154} 2 => App\Models\Branch {#1159} 3 => App\Models\Branch {#1163} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1302 #items: array:2 [ 0 => App\Models\Element {#1311 …30} 1 => App\Models\Element {#1313 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319777" "type" => "task" ] "previous" => array:2 [ "refs" => "1319775" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1308 #items: array:1 [ 0 => App\Models\Book {#1122} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319776 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_page_end" => "237" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-131" "field_display_title" => "131" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1297} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1298} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1299} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1300} "content" => Illuminate\Database\Eloquent\Collection {#1302} "next" => array:2 [ "refs" => "1319777" "type" => "task" ] "previous" => array:2 [ "refs" => "1319775" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1308} "page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1341197 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-236" "field_display_title" => "236" "field_folder" => "1" "field_image_name" => "236" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1087} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1086} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1082} "content" => Illuminate\Database\Eloquent\Collection {#1116} "next" => array:2 [ "refs" => "1341198" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341196" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1281} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319775 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "236" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-130" "field_display_title" => "130" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110} "content" => Illuminate\Database\Eloquent\Collection {#1072} "next" => array:2 [ "refs" => "1319776" "type" => "task" ] "previous" => array:2 [ "refs" => "1319774" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1104} "page" => array:2 [ "refs" => "1341197" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№130 (с. 236)
Условие. №130 (с. 236)
скриншот условия
O30. Виток изолированного провода изогнут в виде восьмерки (см. рисунок), так что $r_1 = 20$ мм и $r_2 = 60$ мм. В течение промежутка времени $\Delta t = 0,50$ мс однородное магнитное поле, перпендикулярное плоскости витка, равномерно возрастает от нуля до $B = 5$ Тл. На какое напряжение $\text{U}$ должна быть рассчитана изоляция между проводами, чтобы не произошел ее пробой?
☑ U > 38$ В.
Решение. Обозначим сопротивления верхнего и нижнего колец «восьмерки» соответственно $R_1$ и $R_2$, а индуцируемые в них ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$. Эти ЭДС действуют в цепи навстречу друг другу. Пробой возможен между точками $\text{A}$ и $\text{B}$ на перемычке «восьмерки» (см. эквивалентную схему цепи на рисунке).
Согласно закону Ома
$I = \frac{\mathcal{E}_1 - \mathcal{E}_2}{R_1 + R_2}$, $U_{AB} = \mathcal{E}_2 - I R_2 = \frac{\mathcal{E}_2 R_1 + \mathcal{E}_1 R_2}{R_1 + R_2}$.
Используя закон электромагнитной индукции и учитывая, что $R_2/R_1 = r_2/r_1$, получаем $U_{AB} = \pi B r_1 r_2 / \Delta t = 38$ (В).
О31. Катушка имеет индуктивность $\text{L}$ и электрическое сопро-
Решение. №130 (с. 236)
Дано:
Радиус меньшего кольца, $r_1 = 20 \text{ мм}$
Радиус большего кольца, $r_2 = 60 \text{ мм}$
Промежуток времени, $\Delta t = 0.50 \text{ мс}$
Начальная индукция магнитного поля, $B_0 = 0 \text{ Тл}$
Конечная индукция магнитного поля, $B = 5 \text{ Тл}$
Перевод в систему СИ:
$r_1 = 20 \times 10^{-3} \text{ м} = 0.02 \text{ м}$
$r_2 = 60 \times 10^{-3} \text{ м} = 0.06 \text{ м}$
$\Delta t = 0.50 \times 10^{-3} \text{ с}$
Изменение магнитной индукции, $\Delta B = B - B_0 = 5 \text{ Тл}$
Найти:
Минимальное напряжение $U$, на которое должна быть рассчитана изоляция.
Решение:
При изменении магнитного потока $\Phi$ через замкнутый контур в нем возникает ЭДС индукции $\mathcal{E}$, величина которой определяется законом электромагнитной индукции Фарадея:
$|\mathcal{E}| = \left|-\frac{\Delta \Phi}{\Delta t}\right|$
Магнитный поток через площадку $S$ в однородном магнитном поле, перпендикулярном этой площадке, равен $\Phi = B \cdot S$. Поскольку магнитное поле нарастает равномерно, скорость его изменения постоянна. Тогда ЭДС индукции в контуре можно рассчитать как:
$|\mathcal{E}| = S \cdot \frac{\Delta B}{\Delta t}$
Виток в форме "восьмерки" состоит из двух колец, площади которых $S_1 = \pi r_1^2$ и $S_2 = \pi r_2^2$. Так как провод обходит эти кольца в противоположных направлениях (например, одно по часовой стрелке, а другое — против), то согласно правилу Ленца, индуцируемые в них ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$ будут направлены навстречу друг другу. Электрическая схема такого витка эквивалентна двум источникам ЭДС, соединенным встречно.
ЭДС, индуцируемые в каждом кольце, равны:
$\mathcal{E}_1 = S_1 \frac{\Delta B}{\Delta t} = \pi r_1^2 \frac{\Delta B}{\Delta t}$
$\mathcal{E}_2 = S_2 \frac{\Delta B}{\Delta t} = \pi r_2^2 \frac{\Delta B}{\Delta t}$
Наибольшая разность потенциалов, которая может привести к пробою изоляции, возникает в точке пересечения провода. В эквивалентной схеме это напряжение $U$ на зажимах между двумя источниками. Сопротивления участков провода, образующих кольца ($R_1$ и $R_2$), пропорциональны их длинам, то есть $R \sim L = 2\pi r$. Следовательно, отношение сопротивлений равно отношению радиусов:
$\frac{R_1}{R_2} = \frac{r_1}{r_2}$
Для схемы из двух встречно соединенных источников с ЭДС $\mathcal{E}_1$ и $\mathcal{E}_2$ и внутренними сопротивлениями $R_1$ и $R_2$, напряжение на зажимах $U$ определяется по формуле:
$U = \frac{\mathcal{E}_1 R_2 + \mathcal{E}_2 R_1}{R_1 + R_2}$
Подставим в эту формулу выражения для ЭДС и соотношение сопротивлений:
$U = \frac{(\pi r_1^2 \frac{\Delta B}{\Delta t}) R_2 + (\pi r_2^2 \frac{\Delta B}{\Delta t}) R_1}{R_1 + R_2}$
Вынесем общие множители и разделим числитель и знаменатель на $R_2$:
$U = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 R_2 + r_2^2 R_1}{R_1 + R_2} = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_2^2 (R_1/R_2)}{(R_1/R_2) + 1}$
Подставим $\frac{R_1}{R_2} = \frac{r_1}{r_2}$:
$U = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_2^2 (r_1/r_2)}{(r_1/r_2) + 1} = \pi \frac{\Delta B}{\Delta t} \frac{r_1^2 + r_1 r_2}{(r_1+r_2)/r_2} = \pi \frac{\Delta B}{\Delta t} \frac{r_1(r_1 + r_2)r_2}{r_1+r_2}$
После сокращения получаем простую формулу:
$U = \pi r_1 r_2 \frac{\Delta B}{\Delta t}$
Подставим числовые значения из условия задачи в систему СИ:
$U = \pi \cdot (0.02 \text{ м}) \cdot (0.06 \text{ м}) \cdot \frac{5 \text{ Тл}}{0.50 \times 10^{-3} \text{ с}}$
$U = \pi \cdot 0.0012 \cdot 10^4 = 12\pi \text{ В}$
Вычислим приближенное значение, используя $\pi \approx 3.14159$:
$U \approx 12 \cdot 3.14159 \approx 37.7 \text{ В}$
Округляя результат до двух значащих цифр, получаем 38 В. Это означает, что изоляция должна быть рассчитана на напряжение не менее 38 В, чтобы избежать электрического пробоя.
Ответ: Изоляция должна быть рассчитана на напряжение $U \ge 38 \text{ В}$.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 10-11 класс, для упражнения номер 130 расположенного на странице 236 к задачнику 2008 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №130 (с. 236), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.