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Консультация № 145598
01.10.2008, 08:49
0.00 руб.
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1
Здраствуйте уважаемые эксперты! Помогите пожалуйста еще с несколькими задачами:
1) Цепь состоит из катушки индуктивностью L=0.1 Гн и источника тока. Источник тока отключили, не разрывая цепи. Время, через которое сила тока уменьшится до 0.001 первоначального значения, равно t = 0.07 с. Определить сопротивление катушки.
2) Электрон прошел ускоряющую разность потенциалов U = 800 B и, влетев в однородное магнитное поле B = 47 мТл, стал двигаться по винтовой линии с шагом h = 6 см. Определить радиус R винтовой линии.
3) На двух концентрических сферах радиусом R и 2R равномерно распределены заряды с поверхностными плотностями "сигма1" и "сигма2". Требуется: 1) Используя теорему Остроградского-Гаусса найти зависимость E(r) напряженности электрического поля от расстояния для трех областей (I - внутри меньшей сферы II - между сферами III - вне большой сферы).Принять "сигма1" = -4*"сигма", "сигма2" = "сигма". 2) Вычислить напряженность Е в точке удаленной от центра на расстояние r = 1.5R, и указать направление вектора Е.Принять "сигма" = 50 нКл/(м^2). 3) Построить график E(r)
Заранее большое спасибо.
1) Цепь состоит из катушки индуктивностью L=0.1 Гн и источника тока. Источник тока отключили, не разрывая цепи. Время, через которое сила тока уменьшится до 0.001 первоначального значения, равно t = 0.07 с. Определить сопротивление катушки.
2) Электрон прошел ускоряющую разность потенциалов U = 800 B и, влетев в однородное магнитное поле B = 47 мТл, стал двигаться по винтовой линии с шагом h = 6 см. Определить радиус R винтовой линии.
3) На двух концентрических сферах радиусом R и 2R равномерно распределены заряды с поверхностными плотностями "сигма1" и "сигма2". Требуется: 1) Используя теорему Остроградского-Гаусса найти зависимость E(r) напряженности электрического поля от расстояния для трех областей (I - внутри меньшей сферы II - между сферами III - вне большой сферы).Принять "сигма1" = -4*"сигма", "сигма2" = "сигма". 2) Вычислить напряженность Е в точке удаленной от центра на расстояние r = 1.5R, и указать направление вектора Е.Принять "сигма" = 50 нКл/(м^2). 3) Построить график E(r)
Заранее большое спасибо.
Обсуждение
01.10.2008, 10:35
общий
это ответ
Здравствуйте, Prapor1!
1) После отключения источника мгновенное значение силы тока i убывает в функции времени t по закону i = I0*e-t/T (1), где I0 - первоначальное значение, e - основание натуральных логарифмов, T - "постоянная времени", причём T = L/R (2), где R - сопротивление катушки. (Подробное доказательство см. здесь). Обозначив конечное значение тока через Iк, перепишем (1) в виде: e-t/T = Iк/I0 (1а), или et/T = I0/Iк (2), откуда t/T = LN(I0/Iк) (3). По условию Iк/I0 = 0.001, т.е. I0/Iк = 1/0.001 = 1000; тогда из (3): T = t/LN(I0/Iк) (4), а с учётом (2): R = (L/t)*LN(I0/Iк) = (0.1/0.07)*LN(1000) ≈ 10 Ом (точнее, 9.87).
1) После отключения источника мгновенное значение силы тока i убывает в функции времени t по закону i = I0*e-t/T (1), где I0 - первоначальное значение, e - основание натуральных логарифмов, T - "постоянная времени", причём T = L/R (2), где R - сопротивление катушки. (Подробное доказательство см. здесь). Обозначив конечное значение тока через Iк, перепишем (1) в виде: e-t/T = Iк/I0 (1а), или et/T = I0/Iк (2), откуда t/T = LN(I0/Iк) (3). По условию Iк/I0 = 0.001, т.е. I0/Iк = 1/0.001 = 1000; тогда из (3): T = t/LN(I0/Iк) (4), а с учётом (2): R = (L/t)*LN(I0/Iк) = (0.1/0.07)*LN(1000) ≈ 10 Ом (точнее, 9.87).
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