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Консультация № 194047
30.11.2018, 22:57
0.00 руб.
30.11.2018, 23:15
1
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
помогите решить задачу
Индукция неоднородного магнитного поля изменяется по закону
В = В0 (1 +a r),
где
В0 = 0,01 Тл,
a= 1 м-1,
r - расстояние точки от оси вращения.
В этом поле вращается в горизонтальной плоскости относительно вертикальной оси прямой проводник длиной L = 1 м с постоянной угловой скоростью [$969$] = 50 рад/с. Ось вращения проходит через один из концов проводника, силовые линии магнитного поля вертикальны. Определить э.д.с. индукции, возникающую в проводнике.
помогите решить задачу
Индукция неоднородного магнитного поля изменяется по закону
В = В0 (1 +a r),
где
В0 = 0,01 Тл,
a= 1 м-1,
r - расстояние точки от оси вращения.
В этом поле вращается в горизонтальной плоскости относительно вертикальной оси прямой проводник длиной L = 1 м с постоянной угловой скоростью [$969$] = 50 рад/с. Ось вращения проходит через один из концов проводника, силовые линии магнитного поля вертикальны. Определить э.д.с. индукции, возникающую в проводнике.
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Обсуждение
30.11.2018, 23:39
общий
это ответ
Здравствуйте, lenocvol!
На участке проводника длиной dr, движущемся в магнитном поле с индукцией B со скоростью v перпендикулярно линиям поля, возникает ЭДС индукции
dU = vB dr
При этом скорость на расстоянии r от оси равна
v = [$969$]r
ЭДС равна
U = 0L[$8747$]v(r)B(r) dr = 0L[$8747$][$969$]rB0(1+ar) dr =
= [$969$]B0 0L[$8747$](r+ar2) dr = [$969$]B0(aL3/3+L2/2) =
= 50рад/с[$183$]0,01Тл[$183$](1м[sup]-1[/sup][$183$](1м)3/3+(1м)2/2) = 0,417 В
На участке проводника длиной dr, движущемся в магнитном поле с индукцией B со скоростью v перпендикулярно линиям поля, возникает ЭДС индукции
dU = vB dr
При этом скорость на расстоянии r от оси равна
v = [$969$]r
ЭДС равна
U = 0L[$8747$]v(r)B(r) dr = 0L[$8747$][$969$]rB0(1+ar) dr =
= [$969$]B0 0L[$8747$](r+ar2) dr = [$969$]B0(aL3/3+L2/2) =
= 50рад/с[$183$]0,01Тл[$183$](1м[sup]-1[/sup][$183$](1м)3/3+(1м)2/2) = 0,417 В
5
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