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Консультация № 189355
13.05.2016, 12:06
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Уважаемые эксперты! Пожалуйста, помогите решить задачу:
На деревянном цилиндре имеется обмотка из медной проволоки, масса которой 76г. Расстояние между крайними витками много больше диаметра цилиндра и равно 82 см. Сопротивление обмотки 22 Ом. Найти энергию магнитного поля на оси цилиндра, если по обмотке течет ток 8 А. Удельное сопротивление и плотность меди равны 1,6*10^-8 Ом*м и 8,9*10^3 кг/м^3.
На деревянном цилиндре имеется обмотка из медной проволоки, масса которой 76г. Расстояние между крайними витками много больше диаметра цилиндра и равно 82 см. Сопротивление обмотки 22 Ом. Найти энергию магнитного поля на оси цилиндра, если по обмотке течет ток 8 А. Удельное сопротивление и плотность меди равны 1,6*10^-8 Ом*м и 8,9*10^3 кг/м^3.
Обсуждение
18.05.2016, 01:24
общий
это ответ
Здравствуйте, YarLam125!
Объём меди V=76г/8,9г/см[sup]3[/sup]=8,54 см3=S[$8467$]
удельное сопротивление [$961$]=1,6[$183$]10-8 Ом[$183$]м=1,6[$183$]10-6 Ом[$183$]см
сопротивление R=[$961$][$8467$]/S=22 Ом
перемножаем объём и сопротивление
V[$183$]R=[$961$][$8467$]2
отсюда находим длину повода в обмотке
[$8467$]=[$8730$](V[$183$]R/[$961$])=[$8730$](8,54см[sup]3[/sup][$183$]22Ом/(1,6[$183$]10-6Ом[$183$]см))=1,08[$183$]104 см=108 м
площадь сечения провода S=V/[$8467$]=8,54см[sup]3[/sup]/(1,08[$183$]104 см)=7,88[$183$]10-4 см2=0,0788 мм2=[$960$]d2/4
отсюда толщина провода d=[$8730$](4S/[$960$])=0,317 мм=3,17[$183$]10-4 м
В соленоиде длиной L, имеющем N витков, по которому течёт ток I,
создаётся индукция B=[$956$]0NI/L
и плотность энергии магнитного поля w=B2/2[$956$]0=([$956$]0/2)(NI/L)2
при этом L/N=d - это толщина провода
поэтому w=([$956$]0/2)(I/d)2=4[$960$][$183$]10-7Гн/м[$183$](8А)2/2(3,17[$183$]10-4м)2=400 Дж/м3
Объём меди V=76г/8,9г/см[sup]3[/sup]=8,54 см3=S[$8467$]
удельное сопротивление [$961$]=1,6[$183$]10-8 Ом[$183$]м=1,6[$183$]10-6 Ом[$183$]см
сопротивление R=[$961$][$8467$]/S=22 Ом
перемножаем объём и сопротивление
V[$183$]R=[$961$][$8467$]2
отсюда находим длину повода в обмотке
[$8467$]=[$8730$](V[$183$]R/[$961$])=[$8730$](8,54см[sup]3[/sup][$183$]22Ом/(1,6[$183$]10-6Ом[$183$]см))=1,08[$183$]104 см=108 м
площадь сечения провода S=V/[$8467$]=8,54см[sup]3[/sup]/(1,08[$183$]104 см)=7,88[$183$]10-4 см2=0,0788 мм2=[$960$]d2/4
отсюда толщина провода d=[$8730$](4S/[$960$])=0,317 мм=3,17[$183$]10-4 м
В соленоиде длиной L, имеющем N витков, по которому течёт ток I,
создаётся индукция B=[$956$]0NI/L
и плотность энергии магнитного поля w=B2/2[$956$]0=([$956$]0/2)(NI/L)2
при этом L/N=d - это толщина провода
поэтому w=([$956$]0/2)(I/d)2=4[$960$][$183$]10-7Гн/м[$183$](8А)2/2(3,17[$183$]10-4м)2=400 Дж/м3
5
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