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Консультация № 171845
03.09.2009, 01:05
0.00 руб.
0
4
1
Уважаемые эксперты, прошу помочь.
однослойный соленоид без сердечника длиной 20 см и диаметром 4 см имеет плотностую намотку медным проводом диаметром 0,1 мм. За 0.1с сила тока в нем равномерно убывает с 5А до 0. Определить ЭДС самоиндукции в соленоиде. Ответ и решение.
Спасибо за помощь.
однослойный соленоид без сердечника длиной 20 см и диаметром 4 см имеет плотностую намотку медным проводом диаметром 0,1 мм. За 0.1с сила тока в нем равномерно убывает с 5А до 0. Определить ЭДС самоиндукции в соленоиде. Ответ и решение.
Спасибо за помощь.
Обсуждение
03.09.2009, 11:24
общий
это ответ
Здравствуйте, Шаврин Андрей Сергеевич.
Индуктивность соленоида вычисляется по формуле: L = μ*μ0*N2*S/L0 (1), где L0 = 20 см = 0.2 м - длина, S = π*D2/4 (2) - площадь витка, D = 4 см = 0.04 м - диаметр соленоида, N - число витков, μ - магнитная проницаемость сердечника (в нашем случае μ = 1), μ0 = 4*π*10-7 (3) Гн/м - магнитная постоянная. С другой стороны, N = L0/d (4), где d = 0.1 мм = 10-4 м - диаметр провода. Объединив (1), (2), (3) и (4), получаем: L = π2*10-7*D2*L0/d2 = π2*10-7*0.042*0.2/10-8 = 0.0316 Гн. ЭДС самоиндукции в соленоиде E = -L*(di/dt) (5), где (di/dt) - производная тока по времени, равная, в случае равномерного убывания: (di/dt) = -(I/T) (6), где I = 5 А - начальное значение тока, T = 0.1 с - время убывания, откуда E = L*(I/T) (7), или, подставляя вычисленное значение L: E = 0.0316*(5/0.1) = 1.58 В.
Индуктивность соленоида вычисляется по формуле: L = μ*μ0*N2*S/L0 (1), где L0 = 20 см = 0.2 м - длина, S = π*D2/4 (2) - площадь витка, D = 4 см = 0.04 м - диаметр соленоида, N - число витков, μ - магнитная проницаемость сердечника (в нашем случае μ = 1), μ0 = 4*π*10-7 (3) Гн/м - магнитная постоянная. С другой стороны, N = L0/d (4), где d = 0.1 мм = 10-4 м - диаметр провода. Объединив (1), (2), (3) и (4), получаем: L = π2*10-7*D2*L0/d2 = π2*10-7*0.042*0.2/10-8 = 0.0316 Гн. ЭДС самоиндукции в соленоиде E = -L*(di/dt) (5), где (di/dt) - производная тока по времени, равная, в случае равномерного убывания: (di/dt) = -(I/T) (6), где I = 5 А - начальное значение тока, T = 0.1 с - время убывания, откуда E = L*(I/T) (7), или, подставляя вычисленное значение L: E = 0.0316*(5/0.1) = 1.58 В.
08.12.2015, 20:33
общий
подскажите пожалуйста,у меня задача почти такого же типа,я просто не могу понять отличие самоиндукции от индукции,или у меня такое же решение?вот ссылка на мой вопрос https://rfpro.ru/question/188347,очень жду помощи
08.12.2015, 21:18
общий
Адресаты:
Индукция - возникновение ЭДС в следствие движения проводника в магнитном поле или изменения магнитного потока через контур.
Самоиндукция - возникновение ЭДС в следствие изменения магнитного поля, вызванного изменением силы тока в самом контуре.
Так что да, в данном случае речь про самоиндукцию и это частный случай индукции.
Самоиндукция - возникновение ЭДС в следствие изменения магнитного поля, вызванного изменением силы тока в самом контуре.
Так что да, в данном случае речь про самоиндукцию и это частный случай индукции.
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