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Консультация № 197896
03.03.2020, 20:32
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Протон со скоростью V=1,9 км\с влетает перпендикулярно силовым линиям магнитного поля с индукцией В=0,8 мТл. Найти радиус кривизны его траектории R(в см).
Протон со скоростью V=1,9 км\с влетает перпендикулярно силовым линиям магнитного поля с индукцией В=0,8 мТл. Найти радиус кривизны его траектории R(в см).
Обсуждение
05.03.2020, 11:18
общий
это ответ
Здравствуйте, andrei777!
Дано : Скорость протона V = 1,9 км/с, индукция магнитного поля В = 0,8 мТл,
Угол м-ду векторами скорости и индукции [$945$]=90°.
Вычислить радиус R кривизны траектории в см .
Решение : На заряд q , движущийся со скоростью V в магнитном поле с индукцией B, действует сила Лоренца:
Fл = q·V·B·sin([$945$]) . Тут sin([$945$]) = 1 при [$945$]=90° .
Эта сила искривляет траекторию движения протона. Протон начинает двигаться по окружности радиусом R .
Сила Лоренца равна центро-стремительной силе Fц = m·V2/R
то есть: q·V·B = m·V2/R
Здесь m = 1,67·10-27 кг - масса протона, а q = 1,6·10-19 Кл - заряд протона.
Из выше-формулы получим искомый радиус кривизны
R = m·V / (B·q) = 1,67·10-27·1900 / (0,0008·1,6·10-19) [$8776$] 0,02479 м [$8776$] 2,5 см.
Ответ : Радиус кривизны траектории равен 2,5 см
См учебные статьи "Электромагнитная индукция" Ссылка1 ,
Что такое магнитная индукция ? Ссылка2 .
Решения похожих задач rfpro.ru/question/194636 , rfpro.ru/question/197382 .
Дано : Скорость протона V = 1,9 км/с, индукция магнитного поля В = 0,8 мТл,
Угол м-ду векторами скорости и индукции [$945$]=90°.
Вычислить радиус R кривизны траектории в см .
Решение : На заряд q , движущийся со скоростью V в магнитном поле с индукцией B, действует сила Лоренца:
Fл = q·V·B·sin([$945$]) . Тут sin([$945$]) = 1 при [$945$]=90° .
Эта сила искривляет траекторию движения протона. Протон начинает двигаться по окружности радиусом R .
Сила Лоренца равна центро-стремительной силе Fц = m·V2/R
то есть: q·V·B = m·V2/R
Здесь m = 1,67·10-27 кг - масса протона, а q = 1,6·10-19 Кл - заряд протона.
Из выше-формулы получим искомый радиус кривизны
R = m·V / (B·q) = 1,67·10-27·1900 / (0,0008·1,6·10-19) [$8776$] 0,02479 м [$8776$] 2,5 см.
Ответ : Радиус кривизны траектории равен 2,5 см
См учебные статьи "Электромагнитная индукция" Ссылка1 ,
Что такое магнитная индукция ? Ссылка2 .
Решения похожих задач rfpro.ru/question/194636 , rfpro.ru/question/197382 .
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