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Консультация № 183460
01.06.2011, 03:55
0.00 руб.
01.06.2011, 08:01
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Сплошной эбонитовый шар радиусом R = 5 см несет заряд, равномерно распределенный с объемной плотностью ? = 10 нКл/м3. Определить модуль напряженности Е электрического поля и указать направление в точках: 1) на расстоянии
r1 = 3 см от центра шара; 2) на поверхности шара; 3) на расстоянии r2 = 10 см от центра шара. Построить график зависимости Е(r). Диэлектрическая проницаемость эбонита 2,6.
Сплошной эбонитовый шар радиусом R = 5 см несет заряд, равномерно распределенный с объемной плотностью ? = 10 нКл/м3. Определить модуль напряженности Е электрического поля и указать направление в точках: 1) на расстоянии
r1 = 3 см от центра шара; 2) на поверхности шара; 3) на расстоянии r2 = 10 см от центра шара. Построить график зависимости Е(r). Диэлектрическая проницаемость эбонита 2,6.
Обсуждение
01.06.2011, 07:19
общий
это ответ
Здравствуйте, Анна Юрьевна!
Согласно теореме Гаусса, поток вектора напряженности электростатического поля E через произвольную замкнутую поверхность S, внутри которой содержится заряд q, определяется выражением
В частности, для шара радиуса R с объёмной плотностью заряда [$961$] полный заряд равен q = [$961$]V = 4[$960$][$961$]R[sup]3[/sup]/3. Если заряд распределён симметрично, то вектор напряжённости E направлен вдоль радиуса, а его модуль определяется только расстоянием r до центра шара. В частности, вне шара (r>R) сфера радиуса r охватывает поверхность S = 4[$960$]r[sup]2[/sup] и содержит внутри полный заряд шара, поэтому
откуда
Внутри шара (r[$8804$]R) сфера радиуса r, охватывающая поверхность S = 4[$960$]r[sup]2[/sup], содержит внутри часть заряда шара, равную 4[$960$][$961$]r[sup]3[/sup]/3, откуда
и
В частности, на поверхности шара (r = R)
В нашем случае [$961$] = 10 нКл/м[sup]3[/sup] = 10[sup]-8[/sup] Кл/м[sup]3[/sup], [$949$] = 2.6, R = 5 см = 0.05 м, r[sub]1[/sub] = 3 см = 0.03 м, r[sub]2[/sub] = 10 см = 0.1 м и
Согласно теореме Гаусса, поток вектора напряженности электростатического поля E через произвольную замкнутую поверхность S, внутри которой содержится заряд q, определяется выражением
В частности, для шара радиуса R с объёмной плотностью заряда [$961$] полный заряд равен q = [$961$]V = 4[$960$][$961$]R[sup]3[/sup]/3. Если заряд распределён симметрично, то вектор напряжённости E направлен вдоль радиуса, а его модуль определяется только расстоянием r до центра шара. В частности, вне шара (r>R) сфера радиуса r охватывает поверхность S = 4[$960$]r[sup]2[/sup] и содержит внутри полный заряд шара, поэтому
откуда
Внутри шара (r[$8804$]R) сфера радиуса r, охватывающая поверхность S = 4[$960$]r[sup]2[/sup], содержит внутри часть заряда шара, равную 4[$960$][$961$]r[sup]3[/sup]/3, откуда
и
В частности, на поверхности шара (r = R)
В нашем случае [$961$] = 10 нКл/м[sup]3[/sup] = 10[sup]-8[/sup] Кл/м[sup]3[/sup], [$949$] = 2.6, R = 5 см = 0.05 м, r[sub]1[/sub] = 3 см = 0.03 м, r[sub]2[/sub] = 10 см = 0.1 м и
5
Большое спасибо!!!
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