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Консультация № 199567
10.11.2020, 11:19
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Непроводящая сфера радиусом 3 см заряжена равномерно по поверхности зарядом 2 мкКл. Очень длинная нить, равномерно заряженная с линейной плотностью заряда 1 мкКл/м, расположена вдоль силовой линии поля сферы так, что один ее конец находится на расстоянии 3 см от поверхности сферы. Найти силу взаимодействия сферы и нити.
Непроводящая сфера радиусом 3 см заряжена равномерно по поверхности зарядом 2 мкКл. Очень длинная нить, равномерно заряженная с линейной плотностью заряда 1 мкКл/м, расположена вдоль силовой линии поля сферы так, что один ее конец находится на расстоянии 3 см от поверхности сферы. Найти силу взаимодействия сферы и нити.
Обсуждение
17.11.2020, 03:36
общий
это ответ
Здравствуйте, squirrel!
Напряжённость электростатического поля сферы радиусом R с равномерно распределённым по поверхности зарядом Q на расстоянии r > R от её центра определяется выражением
где [$949$][sub]0[/sub] = 8.8542[$183$]10[sup]-12[/sup] Ф/м - электрическая постоянная. Тогда сила взаимодействия сферы с произвольным точечным зарядом q будет равна
а на достаточно малый отрезок нити с зарядом dq будет действовать сила
Интегрируя по всей длине нити, получаем выражение для силы взаимодействия
Для очень длинной нити с линейной плотностью заряда [$955$], начинающейся на расстоянии l от поверхности сферы, dq = [$955$]dr и R+l < r < +[$8734$], поэтому
В данном случае для R = l = 3 см = 0.03 м, Q = 2 мкКл = 0.000002 Кл и [$955$] = 1 мкКл = 0.000001 Кл сила взаимодействия сферы и нити составит
Напряжённость электростатического поля сферы радиусом R с равномерно распределённым по поверхности зарядом Q на расстоянии r > R от её центра определяется выражением
где [$949$][sub]0[/sub] = 8.8542[$183$]10[sup]-12[/sup] Ф/м - электрическая постоянная. Тогда сила взаимодействия сферы с произвольным точечным зарядом q будет равна
а на достаточно малый отрезок нити с зарядом dq будет действовать сила
Интегрируя по всей длине нити, получаем выражение для силы взаимодействия
Для очень длинной нити с линейной плотностью заряда [$955$], начинающейся на расстоянии l от поверхности сферы, dq = [$955$]dr и R+l < r < +[$8734$], поэтому
В данном случае для R = l = 3 см = 0.03 м, Q = 2 мкКл = 0.000002 Кл и [$955$] = 1 мкКл = 0.000001 Кл сила взаимодействия сферы и нити составит
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