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Консультация № 196700
17.10.2019, 12:54
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1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
В равномерно заряженной плоскости (σ = 5,8 нКл/м2) имеется полусферическое углубление. Определить величину напряжённости электрического поля в центре полусферы.
В равномерно заряженной плоскости (σ = 5,8 нКл/м2) имеется полусферическое углубление. Определить величину напряжённости электрического поля в центре полусферы.
Обсуждение
22.10.2019, 08:29
общий
это ответ
Здравствуйте, dar777!
В общем случае напряжённость электрического поля точечного заряда q на расстоянии r от него определяется выражением
Дифференцируя, для бесконечно малого заряда dq имеем
В частности, для бесконечно малого элемента dS равномерно заряженной поверхности с плотностью заряда [$963$] имеем dq = [$963$] dS, откуда
и напряжённость поля определяется интегралом
(не забываем, что E - векторная величина, имеющая в общем случае три компоненты).
В данном случае S - полусферическая поверхность радиуса R с постоянной плотностью заряда [$963$], поэтому r [$8801$] R и
В силу сферической симметрии достаточно рассмотреть только проекцию вектора E на вертикальную ось Oz (остальные компоненты вектора будут равны 0):
Переходя к сферическим координатам по формуле dS = R[sup]2[/sup]sin [$952$] d[$952$] d[$966$], получаем
Для [$963$] = 5.8 нКл/м[sup]2[/sup] = 5.8[$183$]10[sup]-9[/sup] Кл/м[sup]2[/sup] напряжённость будет равна
В/м.
В общем случае напряжённость электрического поля точечного заряда q на расстоянии r от него определяется выражением
Дифференцируя, для бесконечно малого заряда dq имеем
В частности, для бесконечно малого элемента dS равномерно заряженной поверхности с плотностью заряда [$963$] имеем dq = [$963$] dS, откуда
и напряжённость поля определяется интегралом
(не забываем, что E - векторная величина, имеющая в общем случае три компоненты).
В данном случае S - полусферическая поверхность радиуса R с постоянной плотностью заряда [$963$], поэтому r [$8801$] R и
В силу сферической симметрии достаточно рассмотреть только проекцию вектора E на вертикальную ось Oz (остальные компоненты вектора будут равны 0):
Переходя к сферическим координатам по формуле dS = R[sup]2[/sup]sin [$952$] d[$952$] d[$966$], получаем
Для [$963$] = 5.8 нКл/м[sup]2[/sup] = 5.8[$183$]10[sup]-9[/sup] Кл/м[sup]2[/sup] напряжённость будет равна
В/м.
5
Это самое лучшее решение!
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