题目内容
(12分)如图所示,有一半径为r的圆形有界匀强磁场区域,磁感应强度为B,方向垂直纸面向里,其周围对称放置带有中心孔a、b、c的三个相同的平行板电容器,三个电容器两板间距离均为d,接有相同的电压U,在D处有一静止的电子,质量为m,电荷量为e,释放后从a孔射入匀强磁场中,并先后穿过b、c孔再从a孔穿出回到D处,求:?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039332454971.jpg)
(1)电子在匀强磁场中运动的轨道半径R;
(2)匀强磁场的磁感应强度B;?
(3)电子从D出发到第一次回到D处所用的时间t。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039332454971.jpg)
(1)电子在匀强磁场中运动的轨道半径R;
(2)匀强磁场的磁感应强度B;?
(3)电子从D出发到第一次回到D处所用的时间t。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039332771256.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933245504.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933261933.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039332771256.png)
试题分析:(1)带电粒子在匀强磁场中做匀速圆周运动,从 a点进从b点出,粒子运动的半径和磁场半径的几何关系如下图,可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039332925398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933308699.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933245504.png)
(2)粒子在平行板电容器中从D到A,经加速电场加速
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933355793.png)
粒子在匀强磁场中做匀速圆周运动,洛伦兹力提供向心力即
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933370778.png)
带入
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933245504.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933261933.png)
(3)根据运动电荷在磁场中做匀速圆周运动的周期公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933417767.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933433426.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933448981.png)
而电子在匀强电场中做一类 似竖直上抛运动,所经历的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933464327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933479597.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933495789.png)
因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933511882.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003933526945.png)
故电子从出发至第一次回到出发点D处所用的时间为:?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039335421393.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039332771256.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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