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Консультация № 180263
10.10.2010, 14:46
0.00 руб.
10.10.2010, 15:37
0
3
1
Доброго дня! Пожалуйста помогите решить:
Проводник, имеющий форму параболы y=bx2 находится в однородном магнитном поле с индукцией B, перпендикулярном плоскости чертежа.
Из вершины параболы в момент времени t=0 начинают перемещать перемычку с постоянным ускорением a.
Найти ЭДС индукции в образовавшемся контуре как функцию от y.
Проводник, имеющий форму параболы y=bx2 находится в однородном магнитном поле с индукцией B, перпендикулярном плоскости чертежа.
Из вершины параболы в момент времени t=0 начинают перемещать перемычку с постоянным ускорением a.
Найти ЭДС индукции в образовавшемся контуре как функцию от y.
Обсуждение
10.10.2010, 15:04
общий
это ответ
Здравствуйте, Ankden.
Скорость перемещения стержня dy/dt=at
Координата стержня y=at2/2
Ширина стержня, заключённая между ветвями параболы 2x=2[$8730$](y/b)=2t[$8730$](a/2b)=t[$8730$](2a/b)
скорость увеличения площади контура dS/dt=2x[$183$]dy/dt=at2[$8730$](2a/b)
ЭДС в контуре
E=B[$183$]dS/dt=Bat2[$8730$](2a/b)=2By[$8730$](2a/b)
Скорость перемещения стержня dy/dt=at
Координата стержня y=at2/2
Ширина стержня, заключённая между ветвями параболы 2x=2[$8730$](y/b)=2t[$8730$](a/2b)=t[$8730$](2a/b)
скорость увеличения площади контура dS/dt=2x[$183$]dy/dt=at2[$8730$](2a/b)
ЭДС в контуре
E=B[$183$]dS/dt=Bat2[$8730$](2a/b)=2By[$8730$](2a/b)
5
Спасибо!!!
Неизвестный
17.10.2010, 21:50
общий
Roman Chaplinsky / Химик CH:
Здравствуйте, Roman Chaplinsky!
Извините, а разве здесь х по времени не надо дифференцировать? ИМХО, в общем виде получается dS/dt=d/dt(x*y)=x*dy/dt+y*dx/dt...Или в чем я ошибаюсь?
Здравствуйте, Roman Chaplinsky!
Извините, а разве здесь х по времени не надо дифференцировать? ИМХО, в общем виде получается dS/dt=d/dt(x*y)=x*dy/dt+y*dx/dt...Или в чем я ошибаюсь?
17.10.2010, 22:27
общий
Gerhard:
dS/dt=d/dt(x*y)=x*dy/dt+y*dx/dt...
было бы, если бы контур был прямоугольником, вершины которого двигаются по параболе. А так скорость изменения площади равна скорости скорости движения стержня, помноженной на заключённую между ветвями параболы длину.
Да и потом, вспомните формулу ЭДС=Bvl*cos[$945$] - именно она и выходит таким образом
dS/dt=d/dt(x*y)=x*dy/dt+y*dx/dt...
было бы, если бы контур был прямоугольником, вершины которого двигаются по параболе. А так скорость изменения площади равна скорости скорости движения стержня, помноженной на заключённую между ветвями параболы длину.
Да и потом, вспомните формулу ЭДС=Bvl*cos[$945$] - именно она и выходит таким образом
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