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Консультация № 195515
05.05.2019, 21:41
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Здравствуйте! Прошу помощи в следующем вопросе:
Напряжённость поля, создаваемого зарядом, равномерно распределённым по тонкому прямому стержню, в точке, лежащей на продолжении оси стержня на расстоянии 20 см от ближнего конца, равна 9 кВ/м. Длина стержня 20 см. Найти линейную плотность заряда.
Напряжённость поля, создаваемого зарядом, равномерно распределённым по тонкому прямому стержню, в точке, лежащей на продолжении оси стержня на расстоянии 20 см от ближнего конца, равна 9 кВ/м. Длина стержня 20 см. Найти линейную плотность заряда.
Обсуждение
09.05.2019, 12:50
общий
это ответ
Здравствуйте, mustang289!
Имеем E=9*103 В/м -- напряжённость поля, создаваемого зарядом, равномерно распределённым по прямому стержню длиной l=0,2 м, в точке, лежащей на продолжении оси стержня, на расстоянии a=0,2 м от ближнего конца; [$955$] -- линейная плотность заряда стержня; k=9*109 Н/(м2*Кл2) -- электрическая постоянная.
Выделим на стержне малый участок dr, заряд которого dq=[$955$]dr можно считать точечным. Этот точечный заряд, находясь на расстоянии r от заданной точки, создаёт в ней электрическое поле напряжённостью dE=k[$955$]dr/r2. Чтобы вычислить напряжённость поля, создаваемого в рассматриваемой точке всеми элементарными зарядами, расположенными на стержне, проинтегрируем последнее выражение. Получим
откуда
Имеем E=9*103 В/м -- напряжённость поля, создаваемого зарядом, равномерно распределённым по прямому стержню длиной l=0,2 м, в точке, лежащей на продолжении оси стержня, на расстоянии a=0,2 м от ближнего конца; [$955$] -- линейная плотность заряда стержня; k=9*109 Н/(м2*Кл2) -- электрическая постоянная.
Выделим на стержне малый участок dr, заряд которого dq=[$955$]dr можно считать точечным. Этот точечный заряд, находясь на расстоянии r от заданной точки, создаёт в ней электрическое поле напряжённостью dE=k[$955$]dr/r2. Чтобы вычислить напряжённость поля, создаваемого в рассматриваемой точке всеми элементарными зарядами, расположенными на стержне, проинтегрируем последнее выражение. Получим
E=k[$955$]a[$8747$]a+ldr/r2=k[$955$](1/a-1/(a+l))=k[$955$]l/(a(a+l)),
откуда
[$955$]=Ea(a+l)/(kl)=9*103*0,2*(0,2+0,2)/(9*109*0,2)=(0,2+0,2)/(1*106)=0,4*10-6 (Кл/м)=0,4 мкКл/м.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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