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Консультация № 175189
13.12.2009, 12:01
0.00 руб.
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Уважаемые эксперты решите пожалуйста задачу по физике
Виток, в котором поддерживается постоянная сила тока I=60 А, свободно устанавливается в однородном магнитном поле(В=20мТл). Диаметр витка d=10см. Какую работу А нужно совершить, чтобы повернуть виток относительно оси, совпадающей с диаметром, на угол альфа=Pi/3?
Заранее благодарен!
Виток, в котором поддерживается постоянная сила тока I=60 А, свободно устанавливается в однородном магнитном поле(В=20мТл). Диаметр витка d=10см. Какую работу А нужно совершить, чтобы повернуть виток относительно оси, совпадающей с диаметром, на угол альфа=Pi/3?
Заранее благодарен!
Обсуждение
16.12.2009, 09:46
общий
это ответ
Здравствуйте, S K A L T .
Когда виток свободно устанавливается в однородном магнитном поле, нормаль к его плоскости совпадает по направлению с вектором индукции В. Для удержания витка под текущим углом [size=3]α[/size] к этому направлению надо приложить момент сил M = В*I*S*SIN([size=3]α[/size]) (1), где S = [size=3]π[/size]*d2/4 (2) - площадь витка. Элементарная dA работа при повороте на элементарный угол d[size=3]α[/size] равна: dA = M*d[size=3]α[/size] = В*I*([size=3]π[/size]*d2/4)*SIN([size=3]α[/size])*d[size=3]α[/size] (3). Проинтегрировав (3) от [size=3]α[/size] = 0 до [size=3]α[/size] = [size=3]π[/size]/3 = 60°, получим: A = В*I*([size=3]π[/size]*d2/4)*COS(60°) = 20*10-3*60*([size=3]π[/size]*0.12/4)*0.5 = 4.71*10-3 Дж.
Когда виток свободно устанавливается в однородном магнитном поле, нормаль к его плоскости совпадает по направлению с вектором индукции В. Для удержания витка под текущим углом [size=3]α[/size] к этому направлению надо приложить момент сил M = В*I*S*SIN([size=3]α[/size]) (1), где S = [size=3]π[/size]*d2/4 (2) - площадь витка. Элементарная dA работа при повороте на элементарный угол d[size=3]α[/size] равна: dA = M*d[size=3]α[/size] = В*I*([size=3]π[/size]*d2/4)*SIN([size=3]α[/size])*d[size=3]α[/size] (3). Проинтегрировав (3) от [size=3]α[/size] = 0 до [size=3]α[/size] = [size=3]π[/size]/3 = 60°, получим: A = В*I*([size=3]π[/size]*d2/4)*COS(60°) = 20*10-3*60*([size=3]π[/size]*0.12/4)*0.5 = 4.71*10-3 Дж.
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