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Консультация № 180261
10.10.2010, 14:10
0.00 руб.
10.10.2010, 17:00
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Доброго дня! Пожалуйста помогите решить:
Электрическое поле создаётся тонкой, бесконечно длинной нитью, равномерно заряженной с линейной плотностью заряда т = 10-10 Кл/м. Определить поток вектора напряжённости через цилиндрическую поверхность высотой h = 2 м, ось которой совпадает с нитью.
Электрическое поле создаётся тонкой, бесконечно длинной нитью, равномерно заряженной с линейной плотностью заряда т = 10-10 Кл/м. Определить поток вектора напряжённости через цилиндрическую поверхность высотой h = 2 м, ось которой совпадает с нитью.
Обсуждение
11.10.2010, 11:42
общий
это ответ
Здравствуйте, Ankden!
Дано: τ = 10-10 Кл/м, h = 2 м.
Определить: ФE.
На рисунке показан общий вид поля такой нити. Оно является неоднородным.
Поток вектора напряжённости выражается интегралом
ФE = (S)∫EndS,
где En – проекция вектора E на нормаль к площадке dS.
В нашем случае цилиндр радиуса r соосен с нитью, поэтому направление вектора напряжённости электрического поля совпадает направлением нормали к боковой поверхности цилиндра, и
En = E = τ/(2πε0r).
Площадь боковой поверхности цилиндра
S = 2πrh.
Следовательно,
ФE = ES = τ/(2πε0r) • 2πrh = τh/ε0,
что поле подстановки численных значений величин даёт
ФE = ES = 10-10 • 2/(8,85 • 10-12) ≈ 22,6 (В • м).
Ответ: 22,6 В • м.
С уважением.
Дано: τ = 10-10 Кл/м, h = 2 м.
Определить: ФE.
На рисунке показан общий вид поля такой нити. Оно является неоднородным.
Поток вектора напряжённости выражается интегралом
ФE = (S)∫EndS,
где En – проекция вектора E на нормаль к площадке dS.
В нашем случае цилиндр радиуса r соосен с нитью, поэтому направление вектора напряжённости электрического поля совпадает направлением нормали к боковой поверхности цилиндра, и
En = E = τ/(2πε0r).
Площадь боковой поверхности цилиндра
S = 2πrh.
Следовательно,
ФE = ES = τ/(2πε0r) • 2πrh = τh/ε0,
что поле подстановки численных значений величин даёт
ФE = ES = 10-10 • 2/(8,85 • 10-12) ≈ 22,6 (В • м).
Ответ: 22,6 В • м.
С уважением.
5
Cпасибо!!!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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