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Консультация № 178866
05.06.2010, 12:01
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Здравствуйте,
472. При некоторой силе тока плотность энергии магнитного поля соленоида (без сердечника) w=0,2 Дж/м3. Во сколько раз увеличится плотность энергии этого поля при той же силе тока, если соленоид будет иметь железный сердечник?
472. При некоторой силе тока плотность энергии магнитного поля соленоида (без сердечника) w=0,2 Дж/м3. Во сколько раз увеличится плотность энергии этого поля при той же силе тока, если соленоид будет иметь железный сердечник?
Обсуждение
06.06.2010, 00:31
общий
06.06.2010, 04:09
это ответ
Здравствуйте, max123.
Для длинного соленоида известна следующая зависимость между объемной плотностью энергии w и напряженностью H магнитного поля:
w = μ0μH2/2,
причем величина H пропорциональна силе тока I.
Обозначив через μ1 относительную магнитную проницаемость соленоида без сердечника, а через μ2 – относительную магнитную проницаемость соленоида с железным сердечником, найдем отношение соответствующих плотностей энергии:
w1/w2 = μ0μ1H2/2 : μ0μ2H2/2 = μ1/μ2,
откуда следует, что
w2 = w1 ∙ μ2/μ1.
В нашем случае μ1 = 1 (вакуум), поэтому w2 = w1 ∙ μ[sub]2[/sub], и понятно, что объемная плотность энергии при наличии железного сердечника увеличивается в μ2 раз по сравнению с объемной плотностью энергии в отсутствие сердечника.
Величина μ2 для различных марок железа различна..
С уважением.
Для длинного соленоида известна следующая зависимость между объемной плотностью энергии w и напряженностью H магнитного поля:
w = μ0μH2/2,
причем величина H пропорциональна силе тока I.
Обозначив через μ1 относительную магнитную проницаемость соленоида без сердечника, а через μ2 – относительную магнитную проницаемость соленоида с железным сердечником, найдем отношение соответствующих плотностей энергии:
w1/w2 = μ0μ1H2/2 : μ0μ2H2/2 = μ1/μ2,
откуда следует, что
w2 = w1 ∙ μ2/μ1.
В нашем случае μ1 = 1 (вакуум), поэтому w2 = w1 ∙ μ[sub]2[/sub], и понятно, что объемная плотность энергии при наличии железного сердечника увеличивается в μ2 раз по сравнению с объемной плотностью энергии в отсутствие сердечника.
Величина μ2 для различных марок железа различна..
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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