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Консультация № 197574
14.01.2020, 14:00
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Восемь одинаковых точечных зарядов q массой m каждый расположены в вершинах куба со стороной
L . Заряды одновременно отпускают. Найдите скорости зарядов, которые они приобретут на большом расстоянии друг от друга.
Восемь одинаковых точечных зарядов q массой m каждый расположены в вершинах куба со стороной
L . Заряды одновременно отпускают. Найдите скорости зарядов, которые они приобретут на большом расстоянии друг от друга.
Обсуждение
14.01.2020, 16:28
общий
это ответ
Здравствуйте, d.sokol!
Задачу проще всего решать через энергию. Энергия электростатического взаимодействия двух зарядов равна формула1, где r - расстояние между зарядами. Надо посчитать количество возможных пар зарядов, расположенных в вершинах куба, при этом заряды, находящиеся вдоль одного ребра, друг друга компенсируют и ими можно пренебречь. У куба 6 граней, на каждой грани есть 2 пары зарядов, расположенных по диагонали, расстояние между ними формула2 - итого таких пар 12. Еще остались 4 пары зарядов, расположенных в противоположных вершинах куба, и расстояние между такими зарядами равно диагонали куба формула3. Суммарная энергия электростатического взаимодействия зарядов полностью перейдет в кинетическую энергию восьми зарядов, когда они будут на большом расстоянии друг от друга (в этом случае их взаимодействие между собой станет уже пренебрежимо мало). Таким образом, получаем: формула4;
формула5, откуда формула6
смотри картинку...
Задачу проще всего решать через энергию. Энергия электростатического взаимодействия двух зарядов равна формула1, где r - расстояние между зарядами. Надо посчитать количество возможных пар зарядов, расположенных в вершинах куба, при этом заряды, находящиеся вдоль одного ребра, друг друга компенсируют и ими можно пренебречь. У куба 6 граней, на каждой грани есть 2 пары зарядов, расположенных по диагонали, расстояние между ними формула2 - итого таких пар 12. Еще остались 4 пары зарядов, расположенных в противоположных вершинах куба, и расстояние между такими зарядами равно диагонали куба формула3. Суммарная энергия электростатического взаимодействия зарядов полностью перейдет в кинетическую энергию восьми зарядов, когда они будут на большом расстоянии друг от друга (в этом случае их взаимодействие между собой станет уже пренебрежимо мало). Таким образом, получаем: формула4;
формула5, откуда формула6
смотри картинку...
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