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Консультация № 189386
16.05.2016, 21:01
0.00 руб.
22.05.2016, 18:24
1
2
1
Здравствуйте! Прошу помощи в следующем вопросе:
Уважаемые эксперты, помогите решить задачу, пожалуйста.
Определить магнитный поток, проходящий через квадратную рамку. Сторона которой а.
Дано:
I1 = 30А
I2 = 10А
R = 15 см (возможно в методичке ошибка в букве R? Не могу точно сказать, но на рисунке к задаче R нет)
Уважаемые эксперты, помогите решить задачу, пожалуйста.
Определить магнитный поток, проходящий через квадратную рамку. Сторона которой а.
Дано:
I1 = 30А
I2 = 10А
R = 15 см (возможно в методичке ошибка в букве R? Не могу точно сказать, но на рисунке к задаче R нет)
Прикрепленные файлы:
Обсуждение
22.05.2016, 14:59
общий
Адресаты:
Судя по рисунку, в квадратной рамке проходит ток I. Чему равна его величина?
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.05.2016, 18:45
общий
это ответ
Здравствуйте, Алёнkа!
Бесконечный прямой проводник с током I создаёт на расстоянии r индукцию B=[$956$]0I/2[$960$]r
В пределах рамки расстояние до проводника с током I2 изменяется от a до 2a, а до проводника с током I1 - от 2a до 3a.
Чтобы найти магнитный поток, интегрируем индукцию по площади контура, учитывая разные направления токов в проводах (за положительное направление выбираем магнитный поток, создаваемый током в контуре, текущем в отмесченном на чертеже направлении - в этом случае ток I2 даёт положительный магнитный поток, а ток I1 - отрицательный):
Ф=a[$183$]a2a[$8747$][$956$]0I2/2[$960$]r[$183$]dr-a[$183$]2a3a[$8747$][$956$]0I1/2[$960$]r[$183$]dr=[$956$]0a/2[$960$][$183$](a2a[$8747$]I2/r[$183$]dr-2a3a[$8747$]I1/r[$183$]dr)=
=[$956$]0a/2[$960$][$183$](I2[$183$]ln(2a/a)-I1[$183$]ln(3a/2a))=[$956$]0a/2[$960$][$183$](I2[$183$]ln2-I1[$183$]ln1,5)=2[$183$]10-7Гн/м[$183$]0,15м[$183$](10А[$183$]ln2-30А[$183$]ln1,5)=-1,57[$183$]10-7 Вб
Бесконечный прямой проводник с током I создаёт на расстоянии r индукцию B=[$956$]0I/2[$960$]r
В пределах рамки расстояние до проводника с током I2 изменяется от a до 2a, а до проводника с током I1 - от 2a до 3a.
Чтобы найти магнитный поток, интегрируем индукцию по площади контура, учитывая разные направления токов в проводах (за положительное направление выбираем магнитный поток, создаваемый током в контуре, текущем в отмесченном на чертеже направлении - в этом случае ток I2 даёт положительный магнитный поток, а ток I1 - отрицательный):
Ф=a[$183$]a2a[$8747$][$956$]0I2/2[$960$]r[$183$]dr-a[$183$]2a3a[$8747$][$956$]0I1/2[$960$]r[$183$]dr=[$956$]0a/2[$960$][$183$](a2a[$8747$]I2/r[$183$]dr-2a3a[$8747$]I1/r[$183$]dr)=
=[$956$]0a/2[$960$][$183$](I2[$183$]ln(2a/a)-I1[$183$]ln(3a/2a))=[$956$]0a/2[$960$][$183$](I2[$183$]ln2-I1[$183$]ln1,5)=2[$183$]10-7Гн/м[$183$]0,15м[$183$](10А[$183$]ln2-30А[$183$]ln1,5)=-1,57[$183$]10-7 Вб
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