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Консультация № 183465

01.06.2011, 10:34

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Образование

Здравствуйте! Прошу помощи в следующем вопросе:

Соленоид без сердечника с однослойной обмоткой из проволоки диаметром d = 0,5 мм имеет длину l = 0,4 м и поперечное сечение S = 50 см². Какой ток I течет по обмотке при напряжении U = 10 В, если за время t = 0,5 мс в обмотке соленоида выделяется количество теплоты Q, равное энергии W магнитного поля внутри соленоида? Поле внутри соленоида счи¬тать однородным. (Ответ: I=995 мА)

Обсуждение

Неизвестный

01.06.2011, 10:59

общий

это ответ

Здравствуйте, Анна Юрьевна!
Дано:
d = 0.5 мм = 5*10^-4 м
l = 0.4 м
S = 50 см² = 5*10^-3 м²
U = 10 В
t = 0,5 мс = 5*10^-4 с
Q = W
Найти:
I - ?
Решение:
Q = W - по условию
Q = IUt - закон Джоуля - Ленца в дифферинциальной форме (I = const)
W = B²V / 2[$956$][$956$]₀ = B²V / 2[$956$]₀ - Энергия магнитного поля внутри соленоида (однородное магнитное поле), где [$956$] = 1
V = Sl
где: l = Nd, тогда N = l/d
B = [$956$]₀ NI / l = [$956$]₀ I / d, тогда энергия магнитного поля:
W = [$956$]₀ ² I²Sl / d²*2 [$956$]₀ = [$956$]₀I²Sl / d²*2 = Q = IUt
выражаем из этой формулы силу тока:
I = 2Utd² / [$956$]₀ Sl
Подставляя числовые данные получим:
I = 2*10*5*10^-4*( 5*10^-4)² / 4п*10^-7*5*10^-3*0,4 = 995 мА
Ответ: 995 мА

5

Большое спасибо!!!

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