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Консультация № 177520
28.03.2010, 22:31
45.00 руб.
0
1
1
N1 Ось катушки диаметром 10 см, имеющей 1000 витков, расположена горизонтально по магнитному меридиану Земли. По катушке идет ток 0,5 А. Горизонтальная составляющая напряженности
магнитного поля Земли 16 А/м. Какую работу надо произвести, чтобы повернуть катушку на 180°?
магнитного поля Земли 16 А/м. Какую работу надо произвести, чтобы повернуть катушку на 180°?
Обсуждение
29.03.2010, 06:01
общий
12.04.2010, 18:29
это ответ
Здравствуйте, Antonr.
На контур с током в магнитном поле действует механический момент
M=p(m)Bsinф
По условию задачи, в начальном положении контур свободно установился в магнитном поле. При этом момент сил равен нулю, а значит ф=0.
Для подсчета работы применим формулу в дифференциальной форме
dA=Mdф
Подставив сюда выражение M и учтя, что p(m)=ISN=I*пи*R^2*N=I*пи*D^2/4*N
получим
dA=I*B*пи*D^2/4*N*sinф*dф
Взяв интеграл от этого выражения, найдем работу при повороте на конечный угол:
A=I*B*пи*D^2/4*N*интеграл от 0 до 180 от (sinф*dф)=I*B*пи*D^2/4*N*(-cosф) от 0 до 180 = 2*I*B*пи*D^2/4*N
Вычислим искомую величину:
A=0,5*16*4*пи*10-7*3,14*2*0,01*1000/4=125,6 0,000158 (Дж)
На контур с током в магнитном поле действует механический момент
M=p(m)Bsinф
По условию задачи, в начальном положении контур свободно установился в магнитном поле. При этом момент сил равен нулю, а значит ф=0.
Для подсчета работы применим формулу в дифференциальной форме
dA=Mdф
Подставив сюда выражение M и учтя, что p(m)=ISN=I*пи*R^2*N=I*пи*D^2/4*N
получим
dA=I*B*пи*D^2/4*N*sinф*dф
Взяв интеграл от этого выражения, найдем работу при повороте на конечный угол:
A=I*B*пи*D^2/4*N*интеграл от 0 до 180 от (sinф*dф)=I*B*пи*D^2/4*N*(-cosф) от 0 до 180 = 2*I*B*пи*D^2/4*N
Вычислим искомую величину:
A=0,5*16*4*пи*10-7*3,14*2*0,01*1000/4=
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