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Консультация № 184294
21.10.2011, 17:37
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Здравствуйте! Прошу помощи в следующем вопросе:
Два круговых витка радиусом R=4 см каждый
расположены в параллельных плоскостях на расстоянии d =5 см друг от друга. По виткам текут токи I1=I2=4 A.
Найти напряженность H магнитного поля в центре одного
из витков.
Задачу решить, когда:
а) токи в витках текут в одном направлении;
б) токи в витках текут в противоположных направлениях.
Заранее спасибо
Два круговых витка радиусом R=4 см каждый
расположены в параллельных плоскостях на расстоянии d =5 см друг от друга. По виткам текут токи I1=I2=4 A.
Найти напряженность H магнитного поля в центре одного
из витков.
Задачу решить, когда:
а) токи в витках текут в одном направлении;
б) токи в витках текут в противоположных направлениях.
Заранее спасибо
Обсуждение
21.10.2011, 18:16
общий
это ответ
Здравствуйте, Петров Игорь Андреевич!
Дано:
R=4 см =0.04 м
d=5 см = 0.05 м
I1=I2=4A
--------------------
H-?
Решение:
Согласно принципу суперпозиции напряженность в точке С равна H=H1+H2 (в векторном виде, над каждым H значек вектора)
Где H1=I1/(2*R1)
H2=I2*R22/(2*(R22+d2)3/2) (по этой ссылке можно найти вывод формулы)
а)Если токи текут в одном направлении, то H=H1+H2 (без векторов)
У нас R=R1=R2
I1=I2=I
тогда
H=I/(2R)+I*R2/(2*(R2+d2)3/2)
Подставим численные значения
H=4A/(2*0.04 см)+4А*(0.04 см)2/(2*((0.04 см)2+(0.05 см)2)3/2)=62.3 А/м
б) Если токи текут в разных направлениях
то H=H1-H2
H=I/(2R)-I*R2/(2*(R2+d2)3/2)
H=4A/(2*0.04 см)-4А*(0.04 см)2/(2*((0.04 см)2+(0.05 см)2)3/2)=37.7 А/м
Ответ: а)H=62.3 А/м б)H=37.7 А/м
Дано:
R=4 см =0.04 м
d=5 см = 0.05 м
I1=I2=4A
--------------------
H-?
Решение:
Согласно принципу суперпозиции напряженность в точке С равна H=H1+H2 (в векторном виде, над каждым H значек вектора)
Где H1=I1/(2*R1)
H2=I2*R22/(2*(R22+d2)3/2) (по этой ссылке можно найти вывод формулы)
а)Если токи текут в одном направлении, то H=H1+H2 (без векторов)
У нас R=R1=R2
I1=I2=I
тогда
H=I/(2R)+I*R2/(2*(R2+d2)3/2)
Подставим численные значения
H=4A/(2*0.04 см)+4А*(0.04 см)2/(2*((0.04 см)2+(0.05 см)2)3/2)=62.3 А/м
б) Если токи текут в разных направлениях
то H=H1-H2
H=I/(2R)-I*R2/(2*(R2+d2)3/2)
H=4A/(2*0.04 см)-4А*(0.04 см)2/(2*((0.04 см)2+(0.05 см)2)3/2)=37.7 А/м
Ответ: а)H=62.3 А/м б)H=37.7 А/м
Об авторе:
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to live is to die
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