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Консультация № 193487
24.08.2018, 22:09
0.00 руб.
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3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Шаровой источник излучает лучистый поток Фе. Определить лучистые потоки, излучаемые этим источником в зонах углов α1 и α2. В каких ещё десятиградусных зонах излучаются такие же лучистые потоки? Фе = 1257 Вт; α1 = 0 - 10°; α2 = 80 - 90°. Сделать рисунок.
Шаровой источник излучает лучистый поток Фе. Определить лучистые потоки, излучаемые этим источником в зонах углов α1 и α2. В каких ещё десятиградусных зонах излучаются такие же лучистые потоки? Фе = 1257 Вт; α1 = 0 - 10°; α2 = 80 - 90°. Сделать рисунок.
Обсуждение
27.08.2018, 10:25
общий
это ответ
Здравствуйте, dar777!
По условию задачи, источник света излучает одинаковую мощность во всех направлениях. Окружим его сферой радиуса R, как показано на рисунке. Мощность излучения, проходящего через любой участок поверхности сферы, пропорциональна площади этого участка.
Нам требуется определить мощность, излучаемую в углы 0[$186$]<theta<10[$186$], и в углы 80[$186$]<theta<90[$186$].
Площадь поверхности сферического кольца равна Sкольца = 2пR2(cos(theta1) - cos(theta2)). Площадь поверхности сферы Sсферы = 4пR2. Через всю сферу излучается мощность Фe, а через поверхность кольца проходит поток излучения
Ф = Фe *Sкольца/Sсферы. = Фe*(cos(theta1) - cos(theta2))/2.
Подставляя численные значения, находим
Ф0-10 = 9,5 Вт, Ф80-90 = 109,1 Вт.
Очевидно, что такие же значения получатся для углов 170[$186$] < theta < 180[$186$], и для углов 90[$186$] <theta< 100[$186$].
PS. Формулу для площади сферического кольца проще всего получить интегрированием элемента поверхности сферы dS = R2sin(theta)d[$966$]d(theta) по [$966$] от 0 до 2п и по theta от theta1 до theta2. Иначе, можно воспользоваться формулой площади сферического сегмента 2пRh.
По условию задачи, источник света излучает одинаковую мощность во всех направлениях. Окружим его сферой радиуса R, как показано на рисунке. Мощность излучения, проходящего через любой участок поверхности сферы, пропорциональна площади этого участка.
Нам требуется определить мощность, излучаемую в углы 0[$186$]<theta<10[$186$], и в углы 80[$186$]<theta<90[$186$].
Площадь поверхности сферического кольца равна Sкольца = 2пR2(cos(theta1) - cos(theta2)). Площадь поверхности сферы Sсферы = 4пR2. Через всю сферу излучается мощность Фe, а через поверхность кольца проходит поток излучения
Ф = Фe *Sкольца/Sсферы. = Фe*(cos(theta1) - cos(theta2))/2.
Подставляя численные значения, находим
Ф0-10 = 9,5 Вт, Ф80-90 = 109,1 Вт.
Очевидно, что такие же значения получатся для углов 170[$186$] < theta < 180[$186$], и для углов 90[$186$] <theta< 100[$186$].
PS. Формулу для площади сферического кольца проще всего получить интегрированием элемента поверхности сферы dS = R2sin(theta)d[$966$]d(theta) по [$966$] от 0 до 2п и по theta от theta1 до theta2. Иначе, можно воспользоваться формулой площади сферического сегмента 2пRh.
5
Спасибо огромное уважаемый преподаватель! Очень Вам благодарен за квалифицированную помощь.
03.09.2018, 02:07
общий
Адресаты:
У Вас восхитительно эффектный Ответ на трудный Вопрос! К сожалению, одобрить его не могу, поскольку ума не хватает быстро вникнуть и проверить правильность.
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