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Номер 16.9, страница 100 - гдз по физике 8-11 класс учебник, задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Учебник, задачник
Издательство: Илекса
Год издания: 2005 - 2026
Цвет обложки: синий мужчина в красном, летит на черном шаре
ISBN: 978-5-89237-332-6
Популярные ГДЗ в 8 классе
Задачи. Электричество и магнетизм. 16. Электромагнитная индукция - номер 16.9, страница 100.
App\Models\Task {#1024 // 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" => 1288590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "100" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/16-9" "field_display_title" => "16.9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1033 #items: array:1 [ 0 => App\Models\Book {#1030 #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" => 5401 "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 {#1032 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1035 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "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 {#1032 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1035 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1065 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "5" "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 {#1033} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1065} ] #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 {#1066 #items: array:3 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1067 #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" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "68" "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 {#1069 #items: array:1 [ 0 => App\Models\Book {#1070 #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" => 5401 "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 {#1071 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1073 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "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 {#1071 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1073 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1103 #items: array:1 [ 0 => App\Models\Branch {#1104 #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" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_page_start" => "5" "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 {#1106 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1107 …2} ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_page_start" => "5" "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 {#1106 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1107 …2} ] #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" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068} "field_page_start" => "68" "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 {#1069} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1103} ] #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 {#1108 #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" => 1287885 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "16. Электромагнитная индукция" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "99" "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 {#1110 #items: array:1 [ 0 => App\Models\Book {#1111 #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" => 5401 "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 {#1112 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "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 {#1112 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1144 #items: array:1 [ 0 => App\Models\Branch {#1145 #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" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_page_start" => "68" "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 {#1147 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1181 …2} ] #original: array:24 [ "id" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_page_start" => "68" "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 {#1147 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1181 …2} ] #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" => 1287885 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "16. Электромагнитная индукция" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1109} "field_page_start" => "99" "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 {#1110} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144} ] #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 {#1186 #items: array:3 [ 0 => App\Models\Element {#1187 #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" => 1478823 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Edition {#1189 #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" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "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 {#1192 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "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 {#1192 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1194 …2} "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" => "1288590" "type" => "task" ] "text" => "<p><strong>16.9*</strong>. Сверхпроводящее кольцо (см. задачу 16.8) поворачивают относительно горизонтальной оси, не выключая электромагнита. Какой магнитный поток $ \Phi $ будет пронизывать плоскость кольца после поворота на $ 90^\circ $? На $ 180^\circ $? В каком из этих случаев в кольце возникает больший ток?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1435" "height" => 341 "path" => "/media/fizika_08/gelfgat-u/0-16/9-1.webp?ts=1756050026" ] ] ] #original: array:7 [ "id" => 1478823 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1188} "task" => array:2 [ "refs" => "1288590" "type" => "task" ] "text" => "<p><strong>16.9*</strong>. Сверхпроводящее кольцо (см. задачу 16.8) поворачивают относительно горизонтальной оси, не выключая электромагнита. Какой магнитный поток $ \Phi $ будет пронизывать плоскость кольца после поворота на $ 90^\circ $? На $ 180^\circ $? В каком из этих случаев в кольце возникает больший ток?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1435" "height" => 341 "path" => "/media/fizika_08/gelfgat-u/0-16/9-1.webp?ts=1756050026" ] ] ] #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 {#1195 #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" => 1479300 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:1 [ 0 => App\Models\Edition {#1197 #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" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1202 …2} "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" => "1288590" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1446" "height" => 255 "path" => "/media/fizika_08/gelfgat-u/1-16/9-1.webp?ts=1756050091" ] ] ] #original: array:6 [ "id" => 1479300 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1196} "task" => array:2 [ "refs" => "1288590" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1446" "height" => 255 "path" => "/media/fizika_08/gelfgat-u/1-16/9-1.webp?ts=1756050091" ] ] ] #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\Element {#1203 #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" => 1738283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Edition {#1205 #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" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1206 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1206 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1210 …2} "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" => "1288590" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Сверхпроводящее кольцо.<br>Начальный (захваченный) магнитный поток: $\Phi_0$.<br>Угол поворота 1: $\alpha_1 = 90^\circ$.<br>Угол поворота 2: $\alpha_2 = 180^\circ$.</p><p><strong>Найти:</strong></p><p>Магнитный поток после поворота на $90^\circ$: $\Phi_{90}$.<br>Магнитный поток после поворота на $180^\circ$: $\Phi_{180}$.<br>Сравнить токи, возникающие в кольце в этих двух случаях.</p><p><strong>Решение:</strong><br>Ключевое свойство сверхпроводящего контура (кольца) заключается в том, что полный магнитный поток, пронизывающий его, сохраняется. Будем считать, что кольцо перевели в сверхпроводящее состояние, когда оно уже находилось в магнитном поле, и в этот момент его пронизывал магнитный поток $\Phi_0$. Этот поток "захватывается" кольцом и в дальнейшем остается постоянным, пока кольцо находится в сверхпроводящем состоянии.<br>$\Phi_{полный} = \text{const} = \Phi_0$<br>Полный магнитный поток складывается из потока внешнего магнитного поля $\Phi_{внешн}$ и потока собственного магнитного поля, создаваемого током в кольце $\Phi_{собст}$:<br>$\Phi_{полный} = \Phi_{внешн} + \Phi_{собст}$<br>Собственный магнитный поток пропорционален силе тока $\text{I}$ в кольце и его индуктивности $\text{L}$:<br>$\Phi_{собст} = LI$<br>Пусть в начальном положении плоскость кольца перпендикулярна вектору магнитной индукции $\vec{B}$ внешнего поля. Тогда начальный внешний поток равен $\Phi_0 = BS$, где $\text{S}$ — площадь кольца. При этом ток в кольце отсутствует ($I_0=0$), и $\Phi_{собст,0} = 0$.</p><p><strong>Какой магнитный поток Ф будет пронизывать плоскость кольца после поворота на 90°?</strong><br>Согласно закону сохранения магнитного потока для сверхпроводника, полный магнитный поток через кольцо не изменится и останется равным начальному значению $\Phi_0$.<br><strong>Ответ:</strong> Полный магнитный поток, пронизывающий плоскость кольца, останется равным начальному потоку $\Phi_0$.</p><p><strong>На 180°?</strong><br>Аналогично предыдущему случаю, полный магнитный поток через кольцо сохранится и будет равен $\Phi_0$.<br><strong>Ответ:</strong> Полный магнитный поток, пронизывающий плоскость кольца, останется равным начальному потоку $\Phi_0$.</p><p><strong>В каком из этих случаев в кольце возникает больший ток?</strong><br>Найдем силу тока для каждого случая.<br>1. <u>Поворот на $90^\circ$.</u><br>После поворота на $90^\circ$ плоскость кольца становится параллельной линиям магнитной индукции внешнего поля. Внешний магнитный поток через кольцо становится равным нулю:<br>$\Phi_{внешн,90} = BS \cos(90^\circ) = 0$.<br>Полный поток сохраняется: $\Phi_{полный} = \Phi_0$.<br>Следовательно, в кольце должен возникнуть ток $I_{90}$, который создаст собственный магнитный поток $\Phi_{собст,90}$, равный $\Phi_0$.<br>$\Phi_{полный} = \Phi_{внешн,90} + \Phi_{собст,90} \Rightarrow \Phi_0 = 0 + \Phi_{собст,90}$<br>$\Phi_{собст,90} = \Phi_0$<br>Так как $\Phi_{собст,90} = LI_{90}$, то сила тока равна:<br>$I_{90} = \frac{\Phi_0}{L}$<br>2. <u>Поворот на $180^\circ$.</u><br>После поворота на $180^\circ$ нормаль к плоскости кольца будет направлена противоположно вектору магнитной индукции. Внешний магнитный поток станет отрицательным:<br>$\Phi_{внешн,180} = BS \cos(180^\circ) = -BS = -\Phi_0$.<br>Полный поток должен сохраниться: $\Phi_{полный} = \Phi_0$.<br>$\Phi_{полный} = \Phi_{внешн,180} + \Phi_{собст,180} \Rightarrow \Phi_0 = -\Phi_0 + \Phi_{собст,180}$<br>Отсюда находим собственный поток, который должен создать ток $I_{180}$:<br>$\Phi_{собст,180} = 2\Phi_0$<br>Сила тока в этом случае равна:<br>$I_{180} = \frac{2\Phi_0}{L}$<br>Сравнивая токи, видим, что $|I_{180}| = 2|I_{90}|$.<br><strong>Ответ:</strong> Больший ток возникает в кольце при повороте на $180^\circ$. Он в два раза больше, чем ток при повороте на $90^\circ$.</p>" ] #original: array:6 [ "id" => 1738283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1204} "task" => array:2 [ "refs" => "1288590" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Сверхпроводящее кольцо.<br>Начальный (захваченный) магнитный поток: $\Phi_0$.<br>Угол поворота 1: $\alpha_1 = 90^\circ$.<br>Угол поворота 2: $\alpha_2 = 180^\circ$.</p><p><strong>Найти:</strong></p><p>Магнитный поток после поворота на $90^\circ$: $\Phi_{90}$.<br>Магнитный поток после поворота на $180^\circ$: $\Phi_{180}$.<br>Сравнить токи, возникающие в кольце в этих двух случаях.</p><p><strong>Решение:</strong><br>Ключевое свойство сверхпроводящего контура (кольца) заключается в том, что полный магнитный поток, пронизывающий его, сохраняется. Будем считать, что кольцо перевели в сверхпроводящее состояние, когда оно уже находилось в магнитном поле, и в этот момент его пронизывал магнитный поток $\Phi_0$. Этот поток "захватывается" кольцом и в дальнейшем остается постоянным, пока кольцо находится в сверхпроводящем состоянии.<br>$\Phi_{полный} = \text{const} = \Phi_0$<br>Полный магнитный поток складывается из потока внешнего магнитного поля $\Phi_{внешн}$ и потока собственного магнитного поля, создаваемого током в кольце $\Phi_{собст}$:<br>$\Phi_{полный} = \Phi_{внешн} + \Phi_{собст}$<br>Собственный магнитный поток пропорционален силе тока $\text{I}$ в кольце и его индуктивности $\text{L}$:<br>$\Phi_{собст} = LI$<br>Пусть в начальном положении плоскость кольца перпендикулярна вектору магнитной индукции $\vec{B}$ внешнего поля. Тогда начальный внешний поток равен $\Phi_0 = BS$, где $\text{S}$ — площадь кольца. При этом ток в кольце отсутствует ($I_0=0$), и $\Phi_{собст,0} = 0$.</p><p><strong>Какой магнитный поток Ф будет пронизывать плоскость кольца после поворота на 90°?</strong><br>Согласно закону сохранения магнитного потока для сверхпроводника, полный магнитный поток через кольцо не изменится и останется равным начальному значению $\Phi_0$.<br><strong>Ответ:</strong> Полный магнитный поток, пронизывающий плоскость кольца, останется равным начальному потоку $\Phi_0$.</p><p><strong>На 180°?</strong><br>Аналогично предыдущему случаю, полный магнитный поток через кольцо сохранится и будет равен $\Phi_0$.<br><strong>Ответ:</strong> Полный магнитный поток, пронизывающий плоскость кольца, останется равным начальному потоку $\Phi_0$.</p><p><strong>В каком из этих случаев в кольце возникает больший ток?</strong><br>Найдем силу тока для каждого случая.<br>1. <u>Поворот на $90^\circ$.</u><br>После поворота на $90^\circ$ плоскость кольца становится параллельной линиям магнитной индукции внешнего поля. Внешний магнитный поток через кольцо становится равным нулю:<br>$\Phi_{внешн,90} = BS \cos(90^\circ) = 0$.<br>Полный поток сохраняется: $\Phi_{полный} = \Phi_0$.<br>Следовательно, в кольце должен возникнуть ток $I_{90}$, который создаст собственный магнитный поток $\Phi_{собст,90}$, равный $\Phi_0$.<br>$\Phi_{полный} = \Phi_{внешн,90} + \Phi_{собст,90} \Rightarrow \Phi_0 = 0 + \Phi_{собст,90}$<br>$\Phi_{собст,90} = \Phi_0$<br>Так как $\Phi_{собст,90} = LI_{90}$, то сила тока равна:<br>$I_{90} = \frac{\Phi_0}{L}$<br>2. <u>Поворот на $180^\circ$.</u><br>После поворота на $180^\circ$ нормаль к плоскости кольца будет направлена противоположно вектору магнитной индукции. Внешний магнитный поток станет отрицательным:<br>$\Phi_{внешн,180} = BS \cos(180^\circ) = -BS = -\Phi_0$.<br>Полный поток должен сохраниться: $\Phi_{полный} = \Phi_0$.<br>$\Phi_{полный} = \Phi_{внешн,180} + \Phi_{собст,180} \Rightarrow \Phi_0 = -\Phi_0 + \Phi_{собст,180}$<br>Отсюда находим собственный поток, который должен создать ток $I_{180}$:<br>$\Phi_{собст,180} = 2\Phi_0$<br>Сила тока в этом случае равна:<br>$I_{180} = \frac{2\Phi_0}{L}$<br>Сравнивая токи, видим, что $|I_{180}| = 2|I_{90}|$.<br><strong>Ответ:</strong> Больший ток возникает в кольце при повороте на $180^\circ$. Он в два раза больше, чем ток при повороте на $90^\circ$.</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" => "1288591" "type" => "task" ] "previous" => array:2 [ "refs" => "1288589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Book {#1212 #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" => 5401 "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 {#1213 #items: array:1 [ 0 => App\Models\Term {#1214 #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 [ …6] "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 [ …6] "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 {#1215 #items: array:4 [ 0 => App\Models\Term {#1216 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #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 {#1217 #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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #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 {#1218 #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 [ …6] "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 [ …6] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] 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Illuminate\Database\Eloquent\Collection {#1220 #items: array:1 [ 0 => App\Models\Term {#1221 #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 {#1222 #items: array:3 [ 0 => App\Models\Term {#1223 #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 {#1224 #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 {#1225 #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 {#1226 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:1 [ 0 => App\Models\Term {#1228 #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" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" …6 ] #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_country" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:1 [ 0 => App\Models\Term {#1230 #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_city" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:1 [ 0 => App\Models\Term {#1232 #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_series" => Illuminate\Database\Eloquent\Collection {#1233 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1234 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1235 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1236 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:1 [ 0 => App\Models\Term {#1238 #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_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1239 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1240 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1241 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1242 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Term {#1244 #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_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 5401 "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 {#1213} "field_class" => Illuminate\Database\Eloquent\Collection {#1215} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1220} "field_author" => Illuminate\Database\Eloquent\Collection {#1222} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1226} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1227} "field_country" => Illuminate\Database\Eloquent\Collection {#1229} "field_city" => Illuminate\Database\Eloquent\Collection {#1231} "field_series" => Illuminate\Database\Eloquent\Collection {#1233} "field_umk" => Illuminate\Database\Eloquent\Collection {#1234} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1235} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1236} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1237} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1239} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1240} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1241} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1242} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1243} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1686 #items: array:1 [ 0 => App\Models\BookPage {#1248 #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" => 1340451 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "100" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-100" "field_display_title" => "100" "field_folder" => "1" "field_image_name" => "100" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1252 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ 0 => App\Models\Book {#1253 #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 [ …50] #original: array:50 [ …50] #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_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1286 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:1 [ 0 => App\Models\Element {#1288 #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 [ …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 } "next" => array:2 [ "refs" => "1340452" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340450" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:7 [ 0 => App\Models\Task {#1297 #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 [ …24] #original: array:24 [ …24] #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\Task {#1522 #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 [ …24] #original: array:24 [ …24] #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\Task {#1553 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1584 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1615 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1646 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1671 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1340451 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "100" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-100" "field_display_title" => "100" "field_folder" => "1" "field_image_name" => "100" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1252} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1250} "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 {#1286} "content" => Illuminate\Database\Eloquent\Collection {#1287} "next" => array:2 [ "refs" => "1340452" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340450" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1296} ] #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" => 1288590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "100" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/16-9" "field_display_title" => "16.9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "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 {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1066} "content" => Illuminate\Database\Eloquent\Collection {#1186} "next" => array:2 [ "refs" => "1288591" "type" => "task" ] "previous" => array:2 [ "refs" => "1288589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1211} "page" => array:2 [ "refs" => "1340451" "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 => "*" ] }
№16.9 (с. 100)
Условие. №16.9 (с. 100)
скриншот условия
16.9*. Сверхпроводящее кольцо (см. задачу 16.8) поворачивают относительно горизонтальной оси, не выключая электромагнита. Какой магнитный поток $ \Phi $ будет пронизывать плоскость кольца после поворота на $ 90^\circ $? На $ 180^\circ $? В каком из этих случаев в кольце возникает больший ток?
Решение. №16.9 (с. 100)
Решение 2. №16.9 (с. 100)
Дано:
Сверхпроводящее кольцо.
Начальный (захваченный) магнитный поток: $\Phi_0$.
Угол поворота 1: $\alpha_1 = 90^\circ$.
Угол поворота 2: $\alpha_2 = 180^\circ$.
Найти:
Магнитный поток после поворота на $90^\circ$: $\Phi_{90}$.
Магнитный поток после поворота на $180^\circ$: $\Phi_{180}$.
Сравнить токи, возникающие в кольце в этих двух случаях.
Решение:
Ключевое свойство сверхпроводящего контура (кольца) заключается в том, что полный магнитный поток, пронизывающий его, сохраняется. Будем считать, что кольцо перевели в сверхпроводящее состояние, когда оно уже находилось в магнитном поле, и в этот момент его пронизывал магнитный поток $\Phi_0$. Этот поток "захватывается" кольцом и в дальнейшем остается постоянным, пока кольцо находится в сверхпроводящем состоянии.
$\Phi_{полный} = \text{const} = \Phi_0$
Полный магнитный поток складывается из потока внешнего магнитного поля $\Phi_{внешн}$ и потока собственного магнитного поля, создаваемого током в кольце $\Phi_{собст}$:
$\Phi_{полный} = \Phi_{внешн} + \Phi_{собст}$
Собственный магнитный поток пропорционален силе тока $\text{I}$ в кольце и его индуктивности $\text{L}$:
$\Phi_{собст} = LI$
Пусть в начальном положении плоскость кольца перпендикулярна вектору магнитной индукции $\vec{B}$ внешнего поля. Тогда начальный внешний поток равен $\Phi_0 = BS$, где $\text{S}$ — площадь кольца. При этом ток в кольце отсутствует ($I_0=0$), и $\Phi_{собст,0} = 0$.
Какой магнитный поток Ф будет пронизывать плоскость кольца после поворота на 90°?
Согласно закону сохранения магнитного потока для сверхпроводника, полный магнитный поток через кольцо не изменится и останется равным начальному значению $\Phi_0$.
Ответ: Полный магнитный поток, пронизывающий плоскость кольца, останется равным начальному потоку $\Phi_0$.
На 180°?
Аналогично предыдущему случаю, полный магнитный поток через кольцо сохранится и будет равен $\Phi_0$.
Ответ: Полный магнитный поток, пронизывающий плоскость кольца, останется равным начальному потоку $\Phi_0$.
В каком из этих случаев в кольце возникает больший ток?
Найдем силу тока для каждого случая.
1. Поворот на $90^\circ$.
После поворота на $90^\circ$ плоскость кольца становится параллельной линиям магнитной индукции внешнего поля. Внешний магнитный поток через кольцо становится равным нулю:
$\Phi_{внешн,90} = BS \cos(90^\circ) = 0$.
Полный поток сохраняется: $\Phi_{полный} = \Phi_0$.
Следовательно, в кольце должен возникнуть ток $I_{90}$, который создаст собственный магнитный поток $\Phi_{собст,90}$, равный $\Phi_0$.
$\Phi_{полный} = \Phi_{внешн,90} + \Phi_{собст,90} \Rightarrow \Phi_0 = 0 + \Phi_{собст,90}$
$\Phi_{собст,90} = \Phi_0$
Так как $\Phi_{собст,90} = LI_{90}$, то сила тока равна:
$I_{90} = \frac{\Phi_0}{L}$
2. Поворот на $180^\circ$.
После поворота на $180^\circ$ нормаль к плоскости кольца будет направлена противоположно вектору магнитной индукции. Внешний магнитный поток станет отрицательным:
$\Phi_{внешн,180} = BS \cos(180^\circ) = -BS = -\Phi_0$.
Полный поток должен сохраниться: $\Phi_{полный} = \Phi_0$.
$\Phi_{полный} = \Phi_{внешн,180} + \Phi_{собст,180} \Rightarrow \Phi_0 = -\Phi_0 + \Phi_{собст,180}$
Отсюда находим собственный поток, который должен создать ток $I_{180}$:
$\Phi_{собст,180} = 2\Phi_0$
Сила тока в этом случае равна:
$I_{180} = \frac{2\Phi_0}{L}$
Сравнивая токи, видим, что $|I_{180}| = 2|I_{90}|$.
Ответ: Больший ток возникает в кольце при повороте на $180^\circ$. Он в два раза больше, чем ток при повороте на $90^\circ$.
Другие задания:
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