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Здравствуйте, уважаемые эксперты. Помогите, пожалуйста, со след. задачей: Две концентрические металлические заряженные сферы радиусами 50 и 100 мм несут на себе заряды 25 нКл и минус 50 нКл. Найти потенциал поля в точках, отстоящих от центра сфер на расстоянии: 10, 75 и 150 мм (я думаю, что надо решать просто по принципу суперпозиции полей, т.е. рассматривать отдельные 2 сферы и просто суммировать результаты потенциалов от каждой... но что-то не уверена, давно не решала задачи по электричеству)
Уразгильдиева Анна: По-моему, так здесь задача про две сферы, независимых друг от друга, т.к. не указано взаимное расположение сфер. Т.е. решаем две аналогичные задачи сначала про одну сферу, потом про другую. Внутри сфер потенциалы всюду одинаковы и равны [$966$]=q/(4*pi*e0*R), R- радиус сферы, pi=3.14, e0=8.85*10-12 Ф/м Вне сфер [$966$]=q/(4*pi*e0*r), r - расстояние от центра сферы до точки
Об авторе:
С уважением shvetski
Неизвестный
21.01.2010, 09:53
общий
что-то мне подсказывает, что все-таки сфера меньшего диаметра в сфере большего... так, что центры их совпадают...
по теореме Гаусса мы найдем напряженности полей внутри сфер. до радиуса меньшей сферы - 0, затем (от меньшей к большей) φ=q1/(4*pi*e0*r^2), за пределами сфер φ=(q1+q2)/(4*pi*e0*r^2). правильно? но мне потом просто не найти потенциал. не могу проинтегрировать с правильными граничными условиями. клинит и все тут... нужно интегрировать последнее выражение? если да, то и получится как-будто рассматриваем отдельно каждую сферу и потом алгебраически складываем потенциалы... или нет? вот где меня сомнения гложут...
Уразгильдиева Анна: Если для Вас использование теоремы Гаусса доставляет проблемы, то найдите потенциалы в заданных точках для каждого из полей, а затем по принципу суперпозиции найдите их сумму для каждой из точек. Суммы, конечно, алгебраические, т. е. с учетом знаков потенциалов.
Об авторе:
Facta loquuntur.
Неизвестный
21.01.2010, 22:55
общий
Спасибо всем.
Андрей Владимирович: мне не доставляет сложности использование теоремы Гаусса, просто хотела проверить свое решение. правильно думаю или нет. теперь уверена, что правильно.
Shvetski: я и пишу, что это напряженности. вопрос был в другом.
Уразгильдиева Анна: Вопрос задачи о потенциалах. Вы пишите формулы [$966$] = ... - [$966$] - это потенциал... А формулы напряженности следует начинать с буквы Е Извините за назойливость
Об авторе:
С уважением shvetski
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