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Номер 34.3, страница 246 - 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. Электромагнитные колебания и волны. 34. Электромагнитное поле. Электромагнитные волны - номер 34.3, страница 246.
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" => 1319790 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "246" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/34-3" "field_display_title" => "34.3" "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" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1045 #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 [ …6] #original: array:6 [ …6] #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_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #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 [ …6] #original: array:6 [ …6] #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_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:3 [ 0 => App\Models\Term {#1049 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1050 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1051 #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 [ …12] #original: array:12 [ …12] #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_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 #connection: "mysql" …29 } ] #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 {#1148 #items: array:3 [ 0 => App\Models\Branch {#1158 #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 {#1159 #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 {#1193 #items: array:1 [ 0 => App\Models\Book {#1160 #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 {#1162 #items: array:1 [ 0 => App\Models\Term {#1161 #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 {#1163 #items: array:2 [ 0 => App\Models\Term {#1164 #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 {#1165 #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 {#1166 #items: array:1 [ 0 => App\Models\Term {#1167 #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 {#1168 #items: array:3 [ 0 => App\Models\Term {#1169 #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 {#1170 #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 {#1171 #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 {#1172 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ 0 => App\Models\Term {#1174 #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 {#1175 #items: array:1 [ 0 => App\Models\Term {#1176 #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 {#1177 #items: array:1 [ 0 => App\Models\Term {#1178 #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 {#1179 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1180 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Term {#1182 #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 {#1183 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1184 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1185 #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 {#1186 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1187 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1188 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:1 [ 0 => App\Models\Term {#1190 #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 {#1162} "field_class" => Illuminate\Database\Eloquent\Collection {#1163} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1166} "field_author" => Illuminate\Database\Eloquent\Collection {#1168} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1172} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1173} "field_country" => Illuminate\Database\Eloquent\Collection {#1175} "field_city" => Illuminate\Database\Eloquent\Collection {#1177} "field_series" => Illuminate\Database\Eloquent\Collection {#1179} "field_umk" => Illuminate\Database\Eloquent\Collection {#1180} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1181} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1183} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1184} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1185} "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 {#1186} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1187} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1188} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1189} "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 {#1191 #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 {#1159} "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 {#1193} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1191} ] #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 {#1192 #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" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1194 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1195 #items: array:1 [ 0 => App\Models\Book {#1160} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1194} "field_page_start" => "241" "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 {#1195} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1196} ] #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 {#1197 #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" => 1319375 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "34. Электромагнитное поле. Электромагнитные волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1198 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "245" "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 {#1199 #items: array:1 [ 0 => App\Models\Book {#1160} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Branch {#1200 #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" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1202 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1201 #items: array:1 [ 0 => App\Models\Book {#1203 …30} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:1 [ 0 => App\Models\Branch {#1235 …30} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1202} "field_page_start" => "241" "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 {#1201} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1234} ] #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" => 1319375 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "34. Электромагнитное поле. Электромагнитные волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1198} "field_page_start" => "245" "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 {#1199} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1241} ] #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 {#1108 #items: array:2 [ 0 => App\Models\Element {#1138 #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" => 1493938 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Edition {#1137 #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 {#1135 #items: array:1 [ 0 => App\Models\Term {#1136 …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 {#1134 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1133 #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 {#1135} "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 {#1134} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1132} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1133} "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" => "1319790" "type" => "task" ] "text" => "<p><strong>34.3.</strong> Почему увеличение дальности радиосвязи с космическими кораблями в три раза требует увеличения мощности передатчика в 9 раз? Во сколько раз следует увеличить мощность передатчика для увеличения дальности радиолокации в три раза? Поглощение энергии при распространении радиоволн не учитывайте.</p><p><strong><em>Решение.</em></strong> Плотность потока энергии $\text{I}$ пропорциональна $P/R^2$, где $\text{P}$ — излучаемая мощность, а $\text{R}$ — расстояние от передатчика. Поскольку величина $\text{I}$, обеспечивающая прием, зависит только от чувствительности приемника, необходимая для данного приемника мощность передатчика пропорциональна $R^2$. При радиолокации цель, отражая пришедший к ней радиосигнал, сама становится вторичным источником радиоволн, мощность которого $P'$ пропорциональна интенсивности дошедшего до цели сигнала, т. е. величине $P/R^2$. Интенсивность же вернувшегося к радиолокатору отраженного сигнала пропорциональна $P'/R^2$, т. е. $P/R^4$. Следовательно, необходимая для радиолокации мощность $\text{P}$ пропорциональна $R^4$. Таким образом, для увеличения дальности радиолокации в три раза потребуется увеличить мощность передатчика в $3^4 = 81$ раз.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1393" "height" => 1125 "path" => "/media/fizika_10/gelfgat-z/0-34/3-1.webp?ts=1756251143" ] ] ] #original: array:7 [ "id" => 1493938 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128} "task" => array:2 [ "refs" => "1319790" "type" => "task" ] "text" => "<p><strong>34.3.</strong> Почему увеличение дальности радиосвязи с космическими кораблями в три раза требует увеличения мощности передатчика в 9 раз? Во сколько раз следует увеличить мощность передатчика для увеличения дальности радиолокации в три раза? Поглощение энергии при распространении радиоволн не учитывайте.</p><p><strong><em>Решение.</em></strong> Плотность потока энергии $\text{I}$ пропорциональна $P/R^2$, где $\text{P}$ — излучаемая мощность, а $\text{R}$ — расстояние от передатчика. Поскольку величина $\text{I}$, обеспечивающая прием, зависит только от чувствительности приемника, необходимая для данного приемника мощность передатчика пропорциональна $R^2$. При радиолокации цель, отражая пришедший к ней радиосигнал, сама становится вторичным источником радиоволн, мощность которого $P'$ пропорциональна интенсивности дошедшего до цели сигнала, т. е. величине $P/R^2$. Интенсивность же вернувшегося к радиолокатору отраженного сигнала пропорциональна $P'/R^2$, т. е. $P/R^4$. Следовательно, необходимая для радиолокации мощность $\text{P}$ пропорциональна $R^4$. Таким образом, для увеличения дальности радиолокации в три раза потребуется увеличить мощность передатчика в $3^4 = 81$ раз.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1393" "height" => 1125 "path" => "/media/fizika_10/gelfgat-z/0-34/3-1.webp?ts=1756251143" ] ] ] #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 {#1131 #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" => 1691495 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Edition {#1130 #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 {#1126 #items: array:1 [ 0 => App\Models\Term {#1129 …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 {#1127 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1125 #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 {#1126} "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 {#1127} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1124} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1125} "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" => "1319790" "type" => "task" ] "text" => "<p><strong>Почему увеличение дальности радиосвязи с космическими кораблями в три раза требует увеличения мощности передатчика в 9 раз?</strong></p><p><strong>Дано:</strong></p><p>Отношение новой дальности радиосвязи к начальной: $\frac{R_2}{R_1} = 3$.</p><p><strong>Найти:</strong></p><p>Отношение требуемой новой мощности передатчика к начальной: $\frac{P_2}{P_1}$.</p><p><strong>Решение:</strong></p><p>Радиосвязь представляет собой одностороннюю передачу сигнала от передатчика к приёмнику. Интенсивность $I$ (плотность потока энергии) электромагнитной волны, излучаемой источником, убывает с расстоянием. Если пренебречь поглощением энергии в среде, то энергия, излучаемая передатчиком мощностью $P$, равномерно распределяется по поверхности сферы радиусом $R$, площадь которой равна $S=4\pi R^2$.</p><p>Следовательно, интенсивность сигнала на расстоянии $R$ от передатчика определяется формулой:</p><p>$I = \frac{P}{4\pi R^2}$</p><p>Из этой зависимости следует, что интенсивность сигнала обратно пропорциональна квадрату расстояния до источника: $I \propto \frac{P}{R^2}$.</p><p>Для успешного приёма сигнала его интенсивность на приёмнике должна быть не меньше некоторого порогового значения $I_{min}$, определяемого чувствительностью приёмного устройства. При увеличении максимальной дальности связи с $R_1$ до $R_2$ интенсивность сигнала на этой дальности должна оставаться прежней ($I_1 = I_2 = I_{min}$).</p><p>Для начальных условий ($P_1, R_1$) и новых условий ($P_2, R_2$) можем записать:</p><p>$I_{min} \propto \frac{P_1}{R_1^2}$ и $I_{min} \propto \frac{P_2}{R_2^2}$</p><p>Отсюда следует равенство:</p><p>$\frac{P_1}{R_1^2} = \frac{P_2}{R_2^2}$</p><p>Выразим отношение мощностей, которое нам нужно найти:</p><p>$\frac{P_2}{P_1} = \frac{R_2^2}{R_1^2} = (\frac{R_2}{R_1})^2$</p><p>По условию, дальность увеличивается в 3 раза, то есть $\frac{R_2}{R_1} = 3$. Подставим это значение:</p><p>$\frac{P_2}{P_1} = 3^2 = 9$</p><p>Таким образом, увеличение дальности связи в 3 раза требует увеличения мощности передатчика в 9 раз, чтобы скомпенсировать ослабление сигнала из-за распространения на большее расстояние.</p><p><strong>Ответ:</strong> Мощность передатчика необходимо увеличить в 9 раз.</p><p><strong>Во сколько раз следует увеличить мощность передатчика для увеличения дальности радиолокации в три раза?</strong></p><p><strong>Дано:</strong></p><p>Отношение новой дальности радиолокации к начальной: $\frac{R_2}{R_1} = 3$.</p><p><strong>Найти:</strong></p><p>Отношение требуемой новой мощности передатчика к начальной: $\frac{P_2}{P_1}$.</p><p><strong>Решение:</strong></p><p>Радиолокация, в отличие от радиосвязи, является двусторонним процессом. Сигнал сначала должен дойти от радара до цели, а затем, отразившись от нее, вернуться обратно к приёмнику радара.</p><p><strong>1.</strong> <i>Распространение сигнала до цели.</i> Интенсивность сигнала $I_{цель}$, достигающего цели на расстоянии $R$ от радара мощностью $P$, обратно пропорциональна квадрату расстояния:</p><p>$I_{цель} \propto \frac{P}{R^2}$</p><p><strong>2.</strong> <i>Отражение сигнала от цели.</i> Цель, на которую падает сигнал, сама становится вторичным источником излучения (переизлучает энергию). Мощность этого отраженного сигнала $P_{отр}$ пропорциональна интенсивности падающего на цель сигнала $I_{цель}$.</p><p>$P_{отр} \propto I_{цель} \propto \frac{P}{R^2}$</p><p><strong>3.</strong> <i>Распространение отраженного сигнала к радару.</i> Отраженный от цели сигнал распространяется обратно к приёмнику радара, снова преодолевая расстояние $R$. Интенсивность принятого радаром сигнала $I_{прием}$ пропорциональна мощности отраженного сигнала $P_{отр}$ и обратно пропорциональна квадрату расстояния $R$:</p><p>$I_{прием} \propto \frac{P_{отр}}{R^2}$</p><p>Теперь объединим эти зависимости, подставив выражение для $P_{отр}$ в последнюю формулу:</p><p>$I_{прием} \propto \frac{(\frac{P}{R^2})}{R^2} = \frac{P}{R^4}$</p><p>Полученная зависимость известна как основное уравнение радиолокации. Она показывает, что интенсивность возвращающегося к радару сигнала обратно пропорциональна четвертой степени расстояния до цели.</p><p>Для обнаружения цели на максимальной дальности интенсивность принимаемого сигнала должна быть равна пороговой чувствительности приёмника $I_{min}$. Следовательно, для начальных ($P_1, R_1$) и новых ($P_2, R_2$) условий имеем:</p><p>$\frac{P_1}{R_1^4} = \frac{P_2}{R_2^4}$</p><p>Отсюда находим искомое отношение мощностей:</p><p>$\frac{P_2}{P_1} = \frac{R_2^4}{R_1^4} = (\frac{R_2}{R_1})^4$</p><p>По условию, дальность увеличивается в 3 раза, т.е. $\frac{R_2}{R_1} = 3$. Подставляем:</p><p>$\frac{P_2}{P_1} = 3^4 = 81$</p><p><strong>Ответ:</strong> Мощность передатчика необходимо увеличить в 81 раз.</p>" ] #original: array:6 [ "id" => 1691495 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1122} "task" => array:2 [ "refs" => "1319790" "type" => "task" ] "text" => "<p><strong>Почему увеличение дальности радиосвязи с космическими кораблями в три раза требует увеличения мощности передатчика в 9 раз?</strong></p><p><strong>Дано:</strong></p><p>Отношение новой дальности радиосвязи к начальной: $\frac{R_2}{R_1} = 3$.</p><p><strong>Найти:</strong></p><p>Отношение требуемой новой мощности передатчика к начальной: $\frac{P_2}{P_1}$.</p><p><strong>Решение:</strong></p><p>Радиосвязь представляет собой одностороннюю передачу сигнала от передатчика к приёмнику. Интенсивность $I$ (плотность потока энергии) электромагнитной волны, излучаемой источником, убывает с расстоянием. Если пренебречь поглощением энергии в среде, то энергия, излучаемая передатчиком мощностью $P$, равномерно распределяется по поверхности сферы радиусом $R$, площадь которой равна $S=4\pi R^2$.</p><p>Следовательно, интенсивность сигнала на расстоянии $R$ от передатчика определяется формулой:</p><p>$I = \frac{P}{4\pi R^2}$</p><p>Из этой зависимости следует, что интенсивность сигнала обратно пропорциональна квадрату расстояния до источника: $I \propto \frac{P}{R^2}$.</p><p>Для успешного приёма сигнала его интенсивность на приёмнике должна быть не меньше некоторого порогового значения $I_{min}$, определяемого чувствительностью приёмного устройства. При увеличении максимальной дальности связи с $R_1$ до $R_2$ интенсивность сигнала на этой дальности должна оставаться прежней ($I_1 = I_2 = I_{min}$).</p><p>Для начальных условий ($P_1, R_1$) и новых условий ($P_2, R_2$) можем записать:</p><p>$I_{min} \propto \frac{P_1}{R_1^2}$ и $I_{min} \propto \frac{P_2}{R_2^2}$</p><p>Отсюда следует равенство:</p><p>$\frac{P_1}{R_1^2} = \frac{P_2}{R_2^2}$</p><p>Выразим отношение мощностей, которое нам нужно найти:</p><p>$\frac{P_2}{P_1} = \frac{R_2^2}{R_1^2} = (\frac{R_2}{R_1})^2$</p><p>По условию, дальность увеличивается в 3 раза, то есть $\frac{R_2}{R_1} = 3$. Подставим это значение:</p><p>$\frac{P_2}{P_1} = 3^2 = 9$</p><p>Таким образом, увеличение дальности связи в 3 раза требует увеличения мощности передатчика в 9 раз, чтобы скомпенсировать ослабление сигнала из-за распространения на большее расстояние.</p><p><strong>Ответ:</strong> Мощность передатчика необходимо увеличить в 9 раз.</p><p><strong>Во сколько раз следует увеличить мощность передатчика для увеличения дальности радиолокации в три раза?</strong></p><p><strong>Дано:</strong></p><p>Отношение новой дальности радиолокации к начальной: $\frac{R_2}{R_1} = 3$.</p><p><strong>Найти:</strong></p><p>Отношение требуемой новой мощности передатчика к начальной: $\frac{P_2}{P_1}$.</p><p><strong>Решение:</strong></p><p>Радиолокация, в отличие от радиосвязи, является двусторонним процессом. Сигнал сначала должен дойти от радара до цели, а затем, отразившись от нее, вернуться обратно к приёмнику радара.</p><p><strong>1.</strong> <i>Распространение сигнала до цели.</i> Интенсивность сигнала $I_{цель}$, достигающего цели на расстоянии $R$ от радара мощностью $P$, обратно пропорциональна квадрату расстояния:</p><p>$I_{цель} \propto \frac{P}{R^2}$</p><p><strong>2.</strong> <i>Отражение сигнала от цели.</i> Цель, на которую падает сигнал, сама становится вторичным источником излучения (переизлучает энергию). Мощность этого отраженного сигнала $P_{отр}$ пропорциональна интенсивности падающего на цель сигнала $I_{цель}$.</p><p>$P_{отр} \propto I_{цель} \propto \frac{P}{R^2}$</p><p><strong>3.</strong> <i>Распространение отраженного сигнала к радару.</i> Отраженный от цели сигнал распространяется обратно к приёмнику радара, снова преодолевая расстояние $R$. Интенсивность принятого радаром сигнала $I_{прием}$ пропорциональна мощности отраженного сигнала $P_{отр}$ и обратно пропорциональна квадрату расстояния $R$:</p><p>$I_{прием} \propto \frac{P_{отр}}{R^2}$</p><p>Теперь объединим эти зависимости, подставив выражение для $P_{отр}$ в последнюю формулу:</p><p>$I_{прием} \propto \frac{(\frac{P}{R^2})}{R^2} = \frac{P}{R^4}$</p><p>Полученная зависимость известна как основное уравнение радиолокации. Она показывает, что интенсивность возвращающегося к радару сигнала обратно пропорциональна четвертой степени расстояния до цели.</p><p>Для обнаружения цели на максимальной дальности интенсивность принимаемого сигнала должна быть равна пороговой чувствительности приёмника $I_{min}$. Следовательно, для начальных ($P_1, R_1$) и новых ($P_2, R_2$) условий имеем:</p><p>$\frac{P_1}{R_1^4} = \frac{P_2}{R_2^4}$</p><p>Отсюда находим искомое отношение мощностей:</p><p>$\frac{P_2}{P_1} = \frac{R_2^4}{R_1^4} = (\frac{R_2}{R_1})^4$</p><p>По условию, дальность увеличивается в 3 раза, т.е. $\frac{R_2}{R_1} = 3$. Подставляем:</p><p>$\frac{P_2}{P_1} = 3^4 = 81$</p><p><strong>Ответ:</strong> Мощность передатчика необходимо увеличить в 81 раз.</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" => "1319791" "type" => "task" ] "previous" => array:2 [ "refs" => "1319789" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Book {#1160} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\BookPage {#1111 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true 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№34.3 (с. 246)
Условие. №34.3 (с. 246)
скриншот условия
34.3. Почему увеличение дальности радиосвязи с космическими кораблями в три раза требует увеличения мощности передатчика в 9 раз? Во сколько раз следует увеличить мощность передатчика для увеличения дальности радиолокации в три раза? Поглощение энергии при распространении радиоволн не учитывайте.
Решение. Плотность потока энергии $\text{I}$ пропорциональна $P/R^2$, где $\text{P}$ — излучаемая мощность, а $\text{R}$ — расстояние от передатчика. Поскольку величина $\text{I}$, обеспечивающая прием, зависит только от чувствительности приемника, необходимая для данного приемника мощность передатчика пропорциональна $R^2$. При радиолокации цель, отражая пришедший к ней радиосигнал, сама становится вторичным источником радиоволн, мощность которого $P'$ пропорциональна интенсивности дошедшего до цели сигнала, т. е. величине $P/R^2$. Интенсивность же вернувшегося к радиолокатору отраженного сигнала пропорциональна $P'/R^2$, т. е. $P/R^4$. Следовательно, необходимая для радиолокации мощность $\text{P}$ пропорциональна $R^4$. Таким образом, для увеличения дальности радиолокации в три раза потребуется увеличить мощность передатчика в $3^4 = 81$ раз.
Решение. №34.3 (с. 246)
Почему увеличение дальности радиосвязи с космическими кораблями в три раза требует увеличения мощности передатчика в 9 раз?
Дано:
Отношение новой дальности радиосвязи к начальной: $\frac{R_2}{R_1} = 3$.
Найти:
Отношение требуемой новой мощности передатчика к начальной: $\frac{P_2}{P_1}$.
Решение:
Радиосвязь представляет собой одностороннюю передачу сигнала от передатчика к приёмнику. Интенсивность $I$ (плотность потока энергии) электромагнитной волны, излучаемой источником, убывает с расстоянием. Если пренебречь поглощением энергии в среде, то энергия, излучаемая передатчиком мощностью $P$, равномерно распределяется по поверхности сферы радиусом $R$, площадь которой равна $S=4\pi R^2$.
Следовательно, интенсивность сигнала на расстоянии $R$ от передатчика определяется формулой:
$I = \frac{P}{4\pi R^2}$
Из этой зависимости следует, что интенсивность сигнала обратно пропорциональна квадрату расстояния до источника: $I \propto \frac{P}{R^2}$.
Для успешного приёма сигнала его интенсивность на приёмнике должна быть не меньше некоторого порогового значения $I_{min}$, определяемого чувствительностью приёмного устройства. При увеличении максимальной дальности связи с $R_1$ до $R_2$ интенсивность сигнала на этой дальности должна оставаться прежней ($I_1 = I_2 = I_{min}$).
Для начальных условий ($P_1, R_1$) и новых условий ($P_2, R_2$) можем записать:
$I_{min} \propto \frac{P_1}{R_1^2}$ и $I_{min} \propto \frac{P_2}{R_2^2}$
Отсюда следует равенство:
$\frac{P_1}{R_1^2} = \frac{P_2}{R_2^2}$
Выразим отношение мощностей, которое нам нужно найти:
$\frac{P_2}{P_1} = \frac{R_2^2}{R_1^2} = (\frac{R_2}{R_1})^2$
По условию, дальность увеличивается в 3 раза, то есть $\frac{R_2}{R_1} = 3$. Подставим это значение:
$\frac{P_2}{P_1} = 3^2 = 9$
Таким образом, увеличение дальности связи в 3 раза требует увеличения мощности передатчика в 9 раз, чтобы скомпенсировать ослабление сигнала из-за распространения на большее расстояние.
Ответ: Мощность передатчика необходимо увеличить в 9 раз.
Во сколько раз следует увеличить мощность передатчика для увеличения дальности радиолокации в три раза?
Дано:
Отношение новой дальности радиолокации к начальной: $\frac{R_2}{R_1} = 3$.
Найти:
Отношение требуемой новой мощности передатчика к начальной: $\frac{P_2}{P_1}$.
Решение:
Радиолокация, в отличие от радиосвязи, является двусторонним процессом. Сигнал сначала должен дойти от радара до цели, а затем, отразившись от нее, вернуться обратно к приёмнику радара.
1. Распространение сигнала до цели. Интенсивность сигнала $I_{цель}$, достигающего цели на расстоянии $R$ от радара мощностью $P$, обратно пропорциональна квадрату расстояния:
$I_{цель} \propto \frac{P}{R^2}$
2. Отражение сигнала от цели. Цель, на которую падает сигнал, сама становится вторичным источником излучения (переизлучает энергию). Мощность этого отраженного сигнала $P_{отр}$ пропорциональна интенсивности падающего на цель сигнала $I_{цель}$.
$P_{отр} \propto I_{цель} \propto \frac{P}{R^2}$
3. Распространение отраженного сигнала к радару. Отраженный от цели сигнал распространяется обратно к приёмнику радара, снова преодолевая расстояние $R$. Интенсивность принятого радаром сигнала $I_{прием}$ пропорциональна мощности отраженного сигнала $P_{отр}$ и обратно пропорциональна квадрату расстояния $R$:
$I_{прием} \propto \frac{P_{отр}}{R^2}$
Теперь объединим эти зависимости, подставив выражение для $P_{отр}$ в последнюю формулу:
$I_{прием} \propto \frac{(\frac{P}{R^2})}{R^2} = \frac{P}{R^4}$
Полученная зависимость известна как основное уравнение радиолокации. Она показывает, что интенсивность возвращающегося к радару сигнала обратно пропорциональна четвертой степени расстояния до цели.
Для обнаружения цели на максимальной дальности интенсивность принимаемого сигнала должна быть равна пороговой чувствительности приёмника $I_{min}$. Следовательно, для начальных ($P_1, R_1$) и новых ($P_2, R_2$) условий имеем:
$\frac{P_1}{R_1^4} = \frac{P_2}{R_2^4}$
Отсюда находим искомое отношение мощностей:
$\frac{P_2}{P_1} = \frac{R_2^4}{R_1^4} = (\frac{R_2}{R_1})^4$
По условию, дальность увеличивается в 3 раза, т.е. $\frac{R_2}{R_1} = 3$. Подставляем:
$\frac{P_2}{P_1} = 3^4 = 81$
Ответ: Мощность передатчика необходимо увеличить в 81 раз.
Другие задания:
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