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Консультация № 171847
03.09.2009, 01:10
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Уважаемые эксперты, прошу помочь.
Две длинные равномерно заряженные нити с линейной плотностью зарядов 6*10-5 Кл/м расположены на расстоянии 0,2м друг от друга. Найти напряженность электрического поля, созданного в точке, удаленной на 0,2 м от каждой нити.
Ответ и решение.
Спасибо за помощь.
Две длинные равномерно заряженные нити с линейной плотностью зарядов 6*10-5 Кл/м расположены на расстоянии 0,2м друг от друга. Найти напряженность электрического поля, созданного в точке, удаленной на 0,2 м от каждой нити.
Ответ и решение.
Спасибо за помощь.
Обсуждение
03.09.2009, 20:44
общий
это ответ
Здравствуйте, Шаврин Андрей Сергеевич.
Напряженность электрического поля, создаваемого бесконечно длинной равномерно заряженной нитью, определяется по формуле (ее можно получить с помощью теоремы Гаусса)
E = k • 2τ/r,
где τ - линейная плотность заряда, r – расстояние от рассматриваемой точки до нити, k - коэффициент пропорциональности,
k = 1/(4πε0) = 9 • 109 м/Ф.
Вектор напряженности направлен по радиусу.
Нетрудно видеть, что поскольку расстояния от заданной точки до нитей равны расстоянию между нитями, то векторы напряженности будут расположены под углом 60° друг к другу. Тогда, согласно принципу суперпозиции и теореме косинусов, абсолютная величина вектора суммарной напряженности равна
EΣ = √[(k • 2τ/r)2 + (k • 2τ/r)2 – 2 ∙ (k • 2τ/r) ∙ cos 120°] = √[(k • 2τ/r)2 + (k • 2τ/r)2 + k • 2τ/r].
Вроде бы так...
Остается только подставить в полученную формулу числовые значения, что не затруднит Вас. Ответ должен получиться в В/м.
С уважением.
Напряженность электрического поля, создаваемого бесконечно длинной равномерно заряженной нитью, определяется по формуле (ее можно получить с помощью теоремы Гаусса)
E = k • 2τ/r,
где τ - линейная плотность заряда, r – расстояние от рассматриваемой точки до нити, k - коэффициент пропорциональности,
k = 1/(4πε0) = 9 • 109 м/Ф.
Вектор напряженности направлен по радиусу.
Нетрудно видеть, что поскольку расстояния от заданной точки до нитей равны расстоянию между нитями, то векторы напряженности будут расположены под углом 60° друг к другу. Тогда, согласно принципу суперпозиции и теореме косинусов, абсолютная величина вектора суммарной напряженности равна
EΣ = √[(k • 2τ/r)2 + (k • 2τ/r)2 – 2 ∙ (k • 2τ/r) ∙ cos 120°] = √[(k • 2τ/r)2 + (k • 2τ/r)2 + k • 2τ/r].
Вроде бы так...
Остается только подставить в полученную формулу числовые значения, что не затруднит Вас. Ответ должен получиться в В/м.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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