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Консультация № 199259
05.10.2020, 09:46
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Здравствуйте! Прошу помощи в следующем вопросе:
На двух коаксиальных цилиндрах R=2см и R=4см распределены заряды с поверхностными плотностями -100нКл/м2 и +50нКл/м2. найти разность потенциалов между цилиндрами
На двух коаксиальных цилиндрах R=2см и R=4см распределены заряды с поверхностными плотностями -100нКл/м2 и +50нКл/м2. найти разность потенциалов между цилиндрами
Обсуждение
06.10.2020, 22:31
общий
это ответ
Здравствуйте, tanya_kosheleva_60!
Дано:
R1=2 см = 2*10-2 м
R2=4 см = 4*10-2 м
[$963$]1 = -100 нКл/м2= -100*10-9Кл/м2
[$963$]2 = 50 нКл/м2= 50*10-9Кл/м2
Найти:
[$916$][$966$]
Решение:
1. Разность потенциалов на обкладках конденсатора
[$916$][$966$]=q/C ...................... (1)
2. Ёмкость цилиндрического конденсатора
С=(2[$960$][$949$][$949$]0*L)/ln(R2/R1) .. (2)
3. Заряд на обкладках
q=[$963$]*S = 2[$960$]R*L*[$963$] ...........(3)
Заряд на обеих обкладках одинаковый: радиус R одной в два раза больше, чем другой, в то же время поверхностная плотность заряда [$963$] в два раза меньше.
4. Подставим выражения (2) и (3) в (1), получим, сократив константы 2[$960$] и длину обкладок L,
[$916$][$966$]=(R*[$963$]/[$949$][$949$]0)*ln(R2/R1) .. (4)
Поскольку диэлектрик не указан, примем [$949$]=1 (вакуум, воздух), [$949$]0=8,85*10-12 Ф/м - электрическая постоянная, R и [$963$] можно взять любые, только чтоб соответствовали друг другу (были с одинаковыми индексами).
Вычисления:
[$916$][$966$]=4*10-2*50*10-9/(1*8,85*10-12)*ln(4/2) = 157 В
Дано:
R1=2 см = 2*10-2 м
R2=4 см = 4*10-2 м
[$963$]1 = -100 нКл/м2= -100*10-9Кл/м2
[$963$]2 = 50 нКл/м2= 50*10-9Кл/м2
Найти:
[$916$][$966$]
Решение:
1. Разность потенциалов на обкладках конденсатора
[$916$][$966$]=q/C ...................... (1)
2. Ёмкость цилиндрического конденсатора
С=(2[$960$][$949$][$949$]0*L)/ln(R2/R1) .. (2)
3. Заряд на обкладках
q=[$963$]*S = 2[$960$]R*L*[$963$] ...........(3)
Заряд на обеих обкладках одинаковый: радиус R одной в два раза больше, чем другой, в то же время поверхностная плотность заряда [$963$] в два раза меньше.
4. Подставим выражения (2) и (3) в (1), получим, сократив константы 2[$960$] и длину обкладок L,
[$916$][$966$]=(R*[$963$]/[$949$][$949$]0)*ln(R2/R1) .. (4)
Поскольку диэлектрик не указан, примем [$949$]=1 (вакуум, воздух), [$949$]0=8,85*10-12 Ф/м - электрическая постоянная, R и [$963$] можно взять любые, только чтоб соответствовали друг другу (были с одинаковыми индексами).
Вычисления:
[$916$][$966$]=4*10-2*50*10-9/(1*8,85*10-12)*ln(4/2) = 157 В
Об авторе:
С уважением
shvetski
С уважением
shvetski
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