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Консультация № 179872
07.09.2010, 22:31
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Здравствуйте Уважаемые Эксперты. Помогите пожалуйста решить задачу.
По двум параллельным проводам текут в противоположных направлениях токи I1=10А и I2=15 А. Расстояние между проводами А=10 см. Определить напряженность H магнитного поля в точке, удаленной от первого провода на r1=15 см и от второго на r2=10 см. (отв. 17,4 А/м)
По двум параллельным проводам текут в противоположных направлениях токи I1=10А и I2=15 А. Расстояние между проводами А=10 см. Определить напряженность H магнитного поля в точке, удаленной от первого провода на r1=15 см и от второго на r2=10 см. (отв. 17,4 А/м)
Обсуждение
08.09.2010, 07:29
общий
это ответ
Здравствуйте, Massimo.
Для нахождения магнитной индукции В в точке воспользуемся принципом суперпозиции магнитных полей. Для этого определим направления магнитных индукций полей, создаваемых каждым проводником с током в отдельности, и сложим их геометрически:
B=B1+B2
Модуль вектора В можно найти по теореме косинусов:
B=[$8730$](B12+B22 - 2B1B2cos[$945$])
Магнитные индукции выражаются соответственно через силу тока и расстояние от проводов до точки:
B1=[$956$]0I/(2пr1)
B2=[$956$]0I/(2пr2)
Подставим выражения в формулу:
B=[$956$]0/(2п)*[$8730$](I12/r12+I22/r22 - 2I1I2cos[$945$]/(r1r2)
С учетом того, что B=[$956$]0H получим:
H=1/(2п)*[$8730$](I12/r12+I22/r22 - 2I1I2cos[$945$]/(r1r2)
Вычислим cos[$945$]. По теореме косинусов запишем
A2=r12+r22 - 2r1r2cos[$945$]
Отсюда
cos[$945$]=(r12+r22 - A2)/(2r1r2)
cos[$945$]=(102+152-102)/(2*10*15)=3/4
Вычислим искомую величину:
H=1/(2*3.14)*[$8730$](102/0.152+152/0.12 - 2*10*15*(3/4)/(0.1*0.15)=17.4 (А/м)
Удачи
Для нахождения магнитной индукции В в точке воспользуемся принципом суперпозиции магнитных полей. Для этого определим направления магнитных индукций полей, создаваемых каждым проводником с током в отдельности, и сложим их геометрически:
B=B1+B2
Модуль вектора В можно найти по теореме косинусов:
B=[$8730$](B12+B22 - 2B1B2cos[$945$])
Магнитные индукции выражаются соответственно через силу тока и расстояние от проводов до точки:
B1=[$956$]0I/(2пr1)
B2=[$956$]0I/(2пr2)
Подставим выражения в формулу:
B=[$956$]0/(2п)*[$8730$](I12/r12+I22/r22 - 2I1I2cos[$945$]/(r1r2)
С учетом того, что B=[$956$]0H получим:
H=1/(2п)*[$8730$](I12/r12+I22/r22 - 2I1I2cos[$945$]/(r1r2)
Вычислим cos[$945$]. По теореме косинусов запишем
A2=r12+r22 - 2r1r2cos[$945$]
Отсюда
cos[$945$]=(r12+r22 - A2)/(2r1r2)
cos[$945$]=(102+152-102)/(2*10*15)=3/4
Вычислим искомую величину:
H=1/(2*3.14)*[$8730$](102/0.152+152/0.12 - 2*10*15*(3/4)/(0.1*0.15)=17.4 (А/м)
Удачи
5
Большое спасибо за помощь!!!
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