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Консультация № 197898

03.03.2020, 20:40

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Образование

Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:

В магнитном поле с индукцией В=1,1 Тл равномерно вращается рамка из 470 витков проволоки. Площадь рамки равна S= 260 сантиметров в квадрате, угловая скорость вращения W=260 рад/с. Найти максимальную ЭДС (В) индукции , возникающую в этой рамке.

Обсуждение

давно

Алексеев Владимир Николаевич

Мастер-Эксперт
259041
7459

06.03.2020, 06:26

общий

это ответ

Здравствуйте, andrei777!
Дано: B = 1.1 Тл , N=470, Площадь S = 260 см² = 0,026 м² , Круговая частота [$969$] = 260 рад/с.
Вычислить Em

Решение : Магнитный поток Ф ч-з каждый виток рамки в функции времени определяется по формуле
Ф(t) = B·S·cos([$969$]·t)
Потокосцепление [$968$](t) = N·Ф(t) = N·B·S·cos([$969$]·t)

По закону Фарадея, ЭДС, индуцируемая в много-витковой рамке, вычисляется по формуле :
E(t) = -d[$968$](t) / dt
Возьмём производную (дифференцируем) :
E(t) = -[$968$](t)' = [-N·B·S·cos([$969$]·t)]' = -N·B·S·[cos([$969$]·t)]' = [$969$]·N·B·S·sin([$969$]·t)
Искомая амплитуда Em = [$969$]·N·B·S = 260·470·1,1·0,026 [$8776$] 3495 В .
Ответ : Максимальная ЭДС индукции в рамке равна 3495 Вольт.

См учебно-методические статьи : "Закон электромагнитной индукции Фарадея" Ссылка1 ,
"Электромагнитная индукция" Ссылка2 ,
Индуктивность Ссылка3 (там про потокосцепление)

Решения похожих задач : rfpro.ru/question/197889 , rfpro.ru/question/195998 , rfpro.ru/question/179430 , rfpro.ru/question/179846

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