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Консультация № 179685

08.08.2010, 13:46

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Образование

Здравствуйте, помогите
Определить потенциал в центре кольца с внешним диаметром D=0,8 м и внутренним диаметром d=0,4 м, если на нём равномерно распределён заряд q=6[$149$]10-7 Кл.

Обсуждение

давно

Киселев Виталий Сергеевич

Академик
324866
619

09.08.2010, 07:22

общий

это ответ

Здравствуйте, ataman.
Прежде всего, определим поверхностную плотность заряда, учитывая равномерность его распределения по площади кольца:
[$963$]=q/[п(R₂² - R₁²)]
В качестве элементарного заряда выберем заряд на тонком кольце радиуса r (R₁[$8804$]r[$8804$]R₂) и толщиной dr:
dq=[$963$]*2пr*dr.
Известно, что потенциал поля элементарного кольца в центре находится по формуле, аналогичной формуле потенциала точечного заряда:
d[$966$]=k*dq/r=k*[$963$]*2пr*dr/r=2пk[$963$]*dr
в соответствии с принципом суперпозиции полей в среде с [$958$]=1 имеем:
[$966$]=_R1^R2[$8747$]d[$966$]=2пk[$963$]*_R1^R2[$8747$]dr=2пk[$963$](R₂ - R₁)=[$963$]/(2[$958$]₀)*(R₂ - R₁)
Подставляя выражение для поверхностной плотности заряда, окончательно получим выражение для искомой величины:
[$966$]=q/[п(R₂² - R₁²)]*1/(2[$958$]₀)*(R₂ - R₁)=q/[2п[$958$]₀(R₂+R₁)]
Вычислим искомую величину:
[$966$]=6*10^-7/[2*3.14*8.85*10^-12(0.8+0.4)]=9 (кВ)

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