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Консультация № 175866
06.01.2010, 20:31
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Здравствуйте эксперты. Прошу помощи.
На продолжении оси тонкого прямого стержня, равномерно заряженного, с линейной плотностью заряда =20 нКл/см на расстоянии а = 20 см от конца стержня находится точечный заряд q = 8 мкКл. Второй конец стержня уходит в бесконечность. Определить силу, действующую на заряд.
На продолжении оси тонкого прямого стержня, равномерно заряженного, с линейной плотностью заряда =20 нКл/см на расстоянии а = 20 см от конца стержня находится точечный заряд q = 8 мкКл. Второй конец стержня уходит в бесконечность. Определить силу, действующую на заряд.
Обсуждение
06.01.2010, 20:48
общий
это ответ
Здравствуйте, prokon.
Небольшой отрезок стержня длиной dl несет на себе заряд dq=[$955$]*dl и действует на заряд q с силой
dF=(1/4[tnr][size=3]πε[/size][/tnr]0)*q*dq/r2=(1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]*dl/l2, где l - расстояние от данного отрезка стержня до заряда.
Интегрируем по длине стержня от l=a=20 см до бесконечности
F=a[$8734$][$8747$](1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]*dl/l2=-(1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]*(1/[$8734$]-1/a)=(1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]/a
F=9*109Н*м[sup]2[/sup]/Кл[sup]2[/sup]*8*10-6Кл*2*10-6Кл/м/0,2м=0,72 Н
Небольшой отрезок стержня длиной dl несет на себе заряд dq=[$955$]*dl и действует на заряд q с силой
dF=(1/4[tnr][size=3]πε[/size][/tnr]0)*q*dq/r2=(1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]*dl/l2, где l - расстояние от данного отрезка стержня до заряда.
Интегрируем по длине стержня от l=a=20 см до бесконечности
F=a[$8734$][$8747$](1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]*dl/l2=-(1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]*(1/[$8734$]-1/a)=(1/4[tnr][size=3]πε[/size][/tnr]0)*q*[$955$]/a
F=9*109Н*м[sup]2[/sup]/Кл[sup]2[/sup]*8*10-6Кл*2*10-6Кл/м/0,2м=0,72 Н
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