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Консультация № 194506
24.01.2019, 18:49
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
5. Оцените какой должна быть толщина металлической пластины, чтобы находящихся в пластине свободных электронов, концентрация которых n = 1022 см-3, не хватило для компенсации внешнего поля напряжённостью E = 300 В/м, направленного перпендикулярно поверхности пластины? Можно ли изготовить такую пластину? Сделать рисунок.
5. Оцените какой должна быть толщина металлической пластины, чтобы находящихся в пластине свободных электронов, концентрация которых n = 1022 см-3, не хватило для компенсации внешнего поля напряжённостью E = 300 В/м, направленного перпендикулярно поверхности пластины? Можно ли изготовить такую пластину? Сделать рисунок.
Обсуждение
29.01.2019, 19:46
общий
это ответ
Здравствуйте, dar777!
Напряжённость поля, создаваемого равномерно заряженной пластиной, равна
где [$961$] - объёмная плотность заряда, d - толщина пластины, [$949$][sub]0[/sub] = 8.8542[$183$]10[sup]-12[/sup] Ф/м - электрическая постоянная. Для свободных электронов с концентрацией n плотность зарядов равна
где e = 1.602[$183$]10[sup]-19[/sup] Кл, откуда
Следовательно, напряжённость поля пластины прямо пропорциональна её толщине, и компенсация внешнего поля напряжённостью E происходит при
или
В данном случае E = 300 В/м, n = 10[sup]22[/sup] см[sup]-3[/sup] = 10[sup]28[/sup] м[sup]-3[/sup] и
Соответственно, поле свободных электронов пластины не сможет скомпенсировать внешнее поле при d < 3.316[$183$]10[sup]-18[/sup] м. Так как данная величина намного меньше размера атома (10[sup]-11[/sup][$247$]10[sup]-9[/sup] м), то изготовить такую пластину невозможно.
Напряжённость поля, создаваемого равномерно заряженной пластиной, равна
где [$961$] - объёмная плотность заряда, d - толщина пластины, [$949$][sub]0[/sub] = 8.8542[$183$]10[sup]-12[/sup] Ф/м - электрическая постоянная. Для свободных электронов с концентрацией n плотность зарядов равна
где e = 1.602[$183$]10[sup]-19[/sup] Кл, откуда
Следовательно, напряжённость поля пластины прямо пропорциональна её толщине, и компенсация внешнего поля напряжённостью E происходит при
или
В данном случае E = 300 В/м, n = 10[sup]22[/sup] см[sup]-3[/sup] = 10[sup]28[/sup] м[sup]-3[/sup] и
Соответственно, поле свободных электронов пластины не сможет скомпенсировать внешнее поле при d < 3.316[$183$]10[sup]-18[/sup] м. Так как данная величина намного меньше размера атома (10[sup]-11[/sup][$247$]10[sup]-9[/sup] м), то изготовить такую пластину невозможно.
5
Это решение оцениваю на отлично!
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