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Консультация № 189381
16.05.2016, 14:53
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Трудности с такой задачей.
В плоскости расположены два бесконечных контура из тонкого провода. Контурные токи равны I1=20А и I2=30А. Определить магнитную индукцию, создаваемую этими токами в точке О. R= 40 см
Трудности с такой задачей.
В плоскости расположены два бесконечных контура из тонкого провода. Контурные токи равны I1=20А и I2=30А. Определить магнитную индукцию, создаваемую этими токами в точке О. R= 40 см
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Обсуждение
22.05.2016, 15:49
общий
это ответ
Здравствуйте, Алёнkа!
Немного раскрасим чертёж
Рассматриваемая точка находится на продолжении выделенных красным участков, поэтому они в ней индукции не создают.
Рассматриваемая точка находится на перпендикуляре, проведённом через концы выделенных синим полубесконечных прямолинейных участков. Если продолжить такой участок до бесконечности в противоположную сторону, то, учитывая симметрию, имеющаяся и достроенная часть создадут на этом перпендикуляре равную индукцию, дающую в сумме индукцию бесконечного повода. Таким образом, каждый из этих полубесконечных участков создаёт в рассматриваемой точке индукцию, равную половине индукции бесконечного провода, то есть [$956$]0I/4[$960$]r
Зелёный участок представляет из себя 3/4 окружности и создаёт в центре 3/4 индукции полного кругового витка, то есть 3[$956$]0I/8r
Индукция всех этих участков направлена вверх перпендикулярно плоскости чертежа. Складываем значения:
B=3[$956$]0I1/8R+[$956$]0I1/4[$960$]R+[$956$]0I2/4[$960$](2R)=([$956$]0/R)((3/8+1/4[$960$])I1+I2/8[$960$])=
=(4[$960$][$183$]10-7Гн/м/0,4м)[$183$]((3/8+1/4[$960$])[$183$]20А+30А/8[$960$])=3,23[$183$]10-5 Тл
Немного раскрасим чертёж
Рассматриваемая точка находится на продолжении выделенных красным участков, поэтому они в ней индукции не создают.
Рассматриваемая точка находится на перпендикуляре, проведённом через концы выделенных синим полубесконечных прямолинейных участков. Если продолжить такой участок до бесконечности в противоположную сторону, то, учитывая симметрию, имеющаяся и достроенная часть создадут на этом перпендикуляре равную индукцию, дающую в сумме индукцию бесконечного повода. Таким образом, каждый из этих полубесконечных участков создаёт в рассматриваемой точке индукцию, равную половине индукции бесконечного провода, то есть [$956$]0I/4[$960$]r
Зелёный участок представляет из себя 3/4 окружности и создаёт в центре 3/4 индукции полного кругового витка, то есть 3[$956$]0I/8r
Индукция всех этих участков направлена вверх перпендикулярно плоскости чертежа. Складываем значения:
B=3[$956$]0I1/8R+[$956$]0I1/4[$960$]R+[$956$]0I2/4[$960$](2R)=([$956$]0/R)((3/8+1/4[$960$])I1+I2/8[$960$])=
=(4[$960$][$183$]10-7Гн/м/0,4м)[$183$]((3/8+1/4[$960$])[$183$]20А+30А/8[$960$])=3,23[$183$]10-5 Тл
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