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Консультация № 171791
01.09.2009, 09:23
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Здравствуйте, уважаемые эксперты!помогите, пожалуйста, решить задачу. Условие следующее:при какой силе тока I в прямолинейном проводе на расстоянии r=5 см от него объемная плотность энергии магнитного поля w=1 м ДЖ^3? Проводник считать бесконечным по длине.
Заранее Вам большое спасибо!
Заранее Вам большое спасибо!
Обсуждение
01.09.2009, 10:55
общий
это ответ
Здравствуйте, sanek-zel.
В данном случае удобнее всего воспользоваться следующим выражением для объемной плотности энергии магнитного поля (см. здесь или здесь): w = μ0*H2/2 (1), где μ0 = 4*π*10-7 В*сек/(А*м) - "магнитная постоянная", H - напряженность магнитного поля, которая на расстоянии r от прямолинейного провода с током I равна: H = I/(2*π*r) (2). Из (1) и (2) получаем требуемое значение тока: I = 2*π*r*√(2*w/μ0) (3). В это выражение надо r подставлять в метрах, а w - в Дж/м³ (джоулях на метр в кубе), т.е. в А*В*сек/м3, тогда значение тока получится в амперах. В Вашем же условии указана какая-то нелепая и непонятная единица. Если считать, что это 1 Дж/м³, то I = 396 А, если же это 1 мДж/м³, то I = 12.5 А.
В данном случае удобнее всего воспользоваться следующим выражением для объемной плотности энергии магнитного поля (см. здесь или здесь): w = μ0*H2/2 (1), где μ0 = 4*π*10-7 В*сек/(А*м) - "магнитная постоянная", H - напряженность магнитного поля, которая на расстоянии r от прямолинейного провода с током I равна: H = I/(2*π*r) (2). Из (1) и (2) получаем требуемое значение тока: I = 2*π*r*√(2*w/μ0) (3). В это выражение надо r подставлять в метрах, а w - в Дж/м³ (джоулях на метр в кубе), т.е. в А*В*сек/м3, тогда значение тока получится в амперах. В Вашем же условии указана какая-то нелепая и непонятная единица. Если считать, что это 1 Дж/м³, то I = 396 А, если же это 1 мДж/м³, то I = 12.5 А.
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