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Консультация № 189094
05.04.2016, 12:46
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
На рисунке изображены сечения трех прямолинейных бесконечно длинных проводников с токами Расстояния АВ=ВС=5 см, токи I1= I2= I и I3= 2I. Найти точку на прямой АС, в которой напряженность магнитного поля, вызванного токами, равна нулю.
На рисунке изображены сечения трех прямолинейных бесконечно длинных проводников с токами Расстояния АВ=ВС=5 см, токи I1= I2= I и I3= 2I. Найти точку на прямой АС, в которой напряженность магнитного поля, вызванного токами, равна нулю.
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Обсуждение
05.04.2016, 22:51
общий
это ответ
Здравствуйте, Радионов Денис Сергеевич!
За начало координат возьмём точку B.
Тогда напряжённость магнитного поля (точнее, её проекцию на вертикальную ось) найдём по формуле
H(x)=(1/2[$960$])(-I1/(x-xA)-I2/(x-xB)+I3/(x-xC))=(1/2[$960$])(-I/(x+a)-I/x+2I/(x-a))=(I/2[$960$])(-1/(x+a)-1/x+2/(x-a))
где a=AB=BC=5см
Для H(x)=0 требуется
-1/(x+a)-1/x+2/(x-a)=0
2/(x-a)=1/(x+a)+1/x
2/(x-a)=(2x+a)/(x(x+a))
2x(x+a)=(2x+a)(x-a)
2x2+2ax=2x2-ax-a2
3ax=-a2
3x=-a
x=-a/3=-5/3 см=-1,67 см
Искомая точка находится на расстоянии 1,67 см слева от точки B
График зависимости напряжённости магнитного поля на прямой AC:
За начало координат возьмём точку B.
Тогда напряжённость магнитного поля (точнее, её проекцию на вертикальную ось) найдём по формуле
H(x)=(1/2[$960$])(-I1/(x-xA)-I2/(x-xB)+I3/(x-xC))=(1/2[$960$])(-I/(x+a)-I/x+2I/(x-a))=(I/2[$960$])(-1/(x+a)-1/x+2/(x-a))
где a=AB=BC=5см
Для H(x)=0 требуется
-1/(x+a)-1/x+2/(x-a)=0
2/(x-a)=1/(x+a)+1/x
2/(x-a)=(2x+a)/(x(x+a))
2x(x+a)=(2x+a)(x-a)
2x2+2ax=2x2-ax-a2
3ax=-a2
3x=-a
x=-a/3=-5/3 см=-1,67 см
Искомая точка находится на расстоянии 1,67 см слева от точки B
График зависимости напряжённости магнитного поля на прямой AC:
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