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Задать вопрос экспертам

Консультация № 195012

17.03.2019, 13:56

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Образование

Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти период малых колебаний дипольной молекулы с электри-
ческим моментом 3,2*10^-30 Кл*м в воздушном конденсаторе, заряженном до
100 В с расстоянием между обкладками 0,5 см. Момент инерции молеку-
лы равен 10^-45
кг*м^2. Заранее благодарю

Обсуждение

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

17.03.2019, 22:31

общий

это ответ

Здравствуйте, 132457681324576813245768zxcvbnm!
Напряженность в конденсаторе E=U/d, где U - напряжение, а d - зазор конденсатора
при отклонении направления диполя с электрическим моментом p от линий электрического поля на угол [$945$] на диполь действует момент силы
M=-Ep[$183$]sin[$945$]=-Up/d[$183$]sin[$945$]
что при моменте инерции J создаёт угловое ускорение
d²[$945$]/dt²=M/J=-Up/Jd[$183$]sin[$945$]
при малом угле отклонения справедливо приближение sin[$945$][$8776$][$945$] и мы получаем дифференциальное уравнение гармонических колебаний
d²[$945$]/dt²=-Up/Jd[$183$][$945$]
как известно, его решение имеет вид [$945$]=A[$183$]sin([$969$]t+[$966$]₀), при этом d²[$945$]/dt²=-[$969$]²[$945$], откуда угловая частота
[$969$]=[$8730$](-(d²[$945$]/dt²)/[$945$])=[$8730$](Up/Jd)
Период колебаний
T=2[$960$]/[$969$]=2[$960$][$8730$](Jd/Up)=2[$960$][$8730$](10^-45кг[$183$]м[sup]2[/sup][$183$]5[$183$]10^-3м/(100В[$183$]3,2[$183$]10^-30Кл[$183$]м)=7,9[$183$]10^-10 с[$8776$]0,8 нс

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