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Консультация № 178867
05.06.2010, 12:16
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Здравствуйте,помогите
470.Определить взаимную индуктивность L12 тороида и проходя¬щего по его оси бес-конечного прямого провода. Тороид имеет прямоугольное сечение ширины a. Внутренний радиус тороида r1, внешний r2. Число витков тороида N. Тороид и провод погружены в среду с проницаемостью
470.Определить взаимную индуктивность L12 тороида и проходя¬щего по его оси бес-конечного прямого провода. Тороид имеет прямоугольное сечение ширины a. Внутренний радиус тороида r1, внешний r2. Число витков тороида N. Тороид и провод погружены в среду с проницаемостью
Обсуждение
06.06.2010, 08:48
общий
это ответ
Здравствуйте, max123.
Обозначим цифрой 1 тороид, цифрой 2 – прямой провод. Тогда взаимную индуктивность тороида и прямого провода можно найти двумя способами:
- как отношение Ф12/I2 магнитного потока Ф12 через тороид, создаваемого только током провода I2, к этому току,
- как отношение Ф21/I1 магнитного потока Ф21 через провод, создаваемого только током тороида I1, к этому току.
Магнитный поток через провод представляет собой поток через полуплоскость, границей которой служит провод. Если провод замкнуть через бесконечность, то описанная полуплоскость и представит собой поверхность, натянутую на образовавшийся контур. Вне тороида поля нет, а внутри тороида
B = μ0μI1N/(2πr),
где r – расстояние от провода.
Поэтому
Ф21 = aμ0μI1N/(2π) ∙ r1∫r2 dr/r = aμ0μI1N/(2π) ∙ ln r2/r1.
Магнитный поток через катушку
Ф12 = aμ0μI2N/(2π) ∙ r1∫r2 dr/r = aμ0μI2N/(2π) ∙ ln r2/r1.
В итоге получаем, что
L12 = L21 = Ф12/I2 = Ф21/I1 = aμ0μN/(2π) ∙ ln r2/r1.
С уважением.
Обозначим цифрой 1 тороид, цифрой 2 – прямой провод. Тогда взаимную индуктивность тороида и прямого провода можно найти двумя способами:
- как отношение Ф12/I2 магнитного потока Ф12 через тороид, создаваемого только током провода I2, к этому току,
- как отношение Ф21/I1 магнитного потока Ф21 через провод, создаваемого только током тороида I1, к этому току.
Магнитный поток через провод представляет собой поток через полуплоскость, границей которой служит провод. Если провод замкнуть через бесконечность, то описанная полуплоскость и представит собой поверхность, натянутую на образовавшийся контур. Вне тороида поля нет, а внутри тороида
B = μ0μI1N/(2πr),
где r – расстояние от провода.
Поэтому
Ф21 = aμ0μI1N/(2π) ∙ r1∫r2 dr/r = aμ0μI1N/(2π) ∙ ln r2/r1.
Магнитный поток через катушку
Ф12 = aμ0μI2N/(2π) ∙ r1∫r2 dr/r = aμ0μI2N/(2π) ∙ ln r2/r1.
В итоге получаем, что
L12 = L21 = Ф12/I2 = Ф21/I1 = aμ0μN/(2π) ∙ ln r2/r1.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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