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дравствуйте мои дорогие эксперты. Очень нужна ваша помощь, меньше недели до сессии. Вот задачка:
Ион, пройдя ускоряющую разность потенциалов 645 В, влетел в скрещенные под прямым углом однородные магнитное (В = 1,5 мТл) и электрическое (Е = 200 В/м) поля. Определить отношение заряда иона к его массе, если ион в этих полях движется прямолинейно.
Обсуждение
Неизвестный
11.02.2009, 16:08
общий
11.02.2009, 18:37
это ответ
Здравствуйте, Мария Романова! Решение: Дано: U =645В; В =1,5мТл =1,5*10^-3Тл; Е = 200 В/м; Данных о характере движения иона не-достаточно! Буду предполагать, что в условии пропущены сведения о РАВНОМЕРНОМ прямолинейном движении иона. На ион действует сила Лоренца FЛ и электрическая сила Еэл. Уравнение движения согласно 2-му закону Ньютона: q*v*B +q*E = m*a, здесь q –заряд иона, B – магнитная индукция магнитного поля, Е – сила, действующая со стороны электрического поля, m – масса иона, а – ускорение. При моем предположении, что движение прямолинейное и равномерное, ускорение после прохо-ждения ускоряющей разности потенциалов U, равно нулю. q*(v*B + E) = 0 (1). Отсюда: q*v*B = - q*E; После сокращения на q: имеем v*B = - E; (2) Выразим импульс m*v через кинетическую энергию иона Екин: m*v = √(2*m*Екин). (3) Но кинетическая энергия иона, прошедшего ускоряющую разность потенциалов U, определяется равенством: Екин = q*U. Подставив это выражение Екин в формулу (3), получим: m*v = √(2*m*q*U). Откуда найдем скорость v = √((2*q*U)/m), (4) Подставим (4) в (2): В*√((2*q*U)/m) = -Е. Возведем в квадрат: (В^2*2*q*U)/m) = Е^2. Разрешив относительно отношения q/m , получим: q/m = (E^2)/(2*B^2*U). Произведем расчет, подставив численные значения задачи: q/m = (4*10^4*В^2/м^2)/(2*2,25*10^-6Тл^2*645В) = 13,78*10^10 Кл/кг.
Неизвестный
11.02.2009, 17:43
общий
это ответ
Здравствуйте, Мария Романова! Эксперт Скоморохов Владимир Иванович дал правильный ход решения, но при вычисления у него, наверное, заглючил калькулятор. Потому, что если я подставляю (Копировать-Вставить) его цифры в свой калькулятор, то у меня получается число q/m = (4*10^4)/(2*2,25*10^-6*645) = 1,378E7= 13.78e6 (Кл/кг)
а не 13,78*10^10 Кл/кг _________________________ Кто из нас прав легко проверить пересчитав размерности из отношения "Кл/кг", в размерность "масса в атомных единицах массы / элементарный заряд".
(m/q)*(qe/me)= (1/1.37e7)*(1.60e-19/1.66e-27)= 7.0 где qe= 1.60e-19 (Кл/эз), элементарный заряд me= 1.66e-27 (кг/аем), атомная единица массы
То есть если выразить массу в аем, а заряд в элементарных зарядах, то отношение массы иона к заряду равно 7. Скорее всего это однократно ионизированный ион лития, или двухкратно ионизированный ион азота.
А если подставить число полученное Скомороховым, то получим (m/q)*(qe/me)= (1/(13,78*10^10))*(1.60e-19/1.66e-27)= 0,0007 непонятно что означающее.
Неизвестный
11.02.2009, 19:38
общий
Да. При вычиcлении получил ) 0,001378*10^10 Кл/кг, а потом при передвижении десятичной запятой множитель 10^10 не изменил. Скоморохов Владимир Иванович
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