问题 计算题

如图所示,用质量为m、总电阻为R的导线做成单匝矩形线框MNPQ,边长PN=2d,PQ=d。该线框置于水平桌面上,线框与桌面间绝缘,它们之间的动摩擦因数为μ。在线框的右侧存在竖直方向的匀强磁场,磁感应强度为B,磁场左右边界aa′、bb′ 间的距离为d,沿aa′ 方向磁场范围足够大。在垂直MN边的水平拉力作用下,线框以速度v匀速向右穿过磁场。在运动中线框平面始终水平,且MN边与磁场的边界平行。求:

(1)MN两点间的电势差;

(2)在线框从MN边进入磁场到MN边穿出磁场的过程中,线框中感应电流产生的焦耳热Q;

(3)在线框从MN边进入磁场到PQ边穿出磁场的过程中,水平拉力对线框所做的功W。

答案

解:(1)线框MN边在磁场中运动时,感应电动势

 

(2)线框中的感应电流

线框MN边在磁场中运动的时间

此过程线框中产生的焦耳热Q=I2Rt=

(3)线框在PQ边穿过磁场的过程中产生的焦耳热Q=

从线框MN边进入磁场到PQ边穿出磁场的过程中,根据动能定理得WF+W+Wf=0

其中W=-2Q=-,Wf=

所以WF=

完形填空
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