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Консультация № 195106
01.04.2019, 17:37
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Здравствуйте! У меня возникли сложности с таким вопросом:
Плоская круглая рамка состоит из 20 витков радиусом 2 см и по ней течет ток в 1 А. Нормаль к рамке составляет угол 90° с направлением магнитного поля напряженностью 30 А/м (воздух). Найти изменение вращающего момента, действующего на рамку, если из 20 витков рамки сделать один круглый виток.
Плоская круглая рамка состоит из 20 витков радиусом 2 см и по ней течет ток в 1 А. Нормаль к рамке составляет угол 90° с направлением магнитного поля напряженностью 30 А/м (воздух). Найти изменение вращающего момента, действующего на рамку, если из 20 витков рамки сделать один круглый виток.
Обсуждение
02.04.2019, 21:10
общий
это ответ
Здравствуйте, Денис!
Вращающий момент равен M=pmB[$183$]sin[$945$]=INSB[$183$]sin[$945$]
где I - ток в рамке, N - число витков, S - площадь витка, B - индукция магнитного поля
При постоянной длине проволоки радиус круглой рамки обратно пропорционален числу витков
[$8467$]=2[$960$]rN
r2/r1=N1/N2
При этом площадь каждого витка прямо пропорциональна квадрату радиуса
S=[$960$]r2
S2/S1=(r2/r1)2=(N1/N2)2
Откуда делаем вывод, что общая площадь всех витков в контуре NS обратно пропорциональна числу витков
N2S2/N1S1=N1/N2
Поскольку общей площади витков прямо пропорционален магнитный момент рамки и действующий на неё момент силы, эти величины также обратно пропорциональны числу витков при постоянной длине проволоки.
M2/M1=N2S2/N1S1=N1/N2
Таким образом, если из N1=20 витков сделать N2=1, вращающий момент силы, действующий на рамку со стороны внешнего магнитного поля, возрастёт в M2/M1=N1/N2=20 раз
Вращающий момент равен M=pmB[$183$]sin[$945$]=INSB[$183$]sin[$945$]
где I - ток в рамке, N - число витков, S - площадь витка, B - индукция магнитного поля
При постоянной длине проволоки радиус круглой рамки обратно пропорционален числу витков
[$8467$]=2[$960$]rN
r2/r1=N1/N2
При этом площадь каждого витка прямо пропорциональна квадрату радиуса
S=[$960$]r2
S2/S1=(r2/r1)2=(N1/N2)2
Откуда делаем вывод, что общая площадь всех витков в контуре NS обратно пропорциональна числу витков
N2S2/N1S1=N1/N2
Поскольку общей площади витков прямо пропорционален магнитный момент рамки и действующий на неё момент силы, эти величины также обратно пропорциональны числу витков при постоянной длине проволоки.
M2/M1=N2S2/N1S1=N1/N2
Таким образом, если из N1=20 витков сделать N2=1, вращающий момент силы, действующий на рамку со стороны внешнего магнитного поля, возрастёт в M2/M1=N1/N2=20 раз
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