题目内容
(15分)如图所示的空间,匀强电场的方向竖直向下,场强为
,匀强磁场的方向水平向外,磁感应强度为
.有两个带电小球A和B都能在垂直于磁场方向的同一竖直平面内做匀速圆周运动(两小球间的库仑力可忽略),运动轨迹如图。已知两个带电小球A和B的质量关系为
,轨道半径为
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250015007434120.png)
(1)试说明小球A和B带什么电,它们所带的电荷量之比
等于多少?
(2)指出小球A和B的绕行方向?
(3)设带电小球A和B在图示位置P处相碰撞,且碰撞后原先在小圆轨道上运动的带电小球B恰好能沿大圆轨道运动,求带电小球A碰撞后所做圆周运动的轨道半径(设碰撞时两个带电小球间电荷量不转移)。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500665351.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500681309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500696560.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500728725.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250015007434120.png)
(1)试说明小球A和B带什么电,它们所带的电荷量之比
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500759471.png)
(2)指出小球A和B的绕行方向?
(3)设带电小球A和B在图示位置P处相碰撞,且碰撞后原先在小圆轨道上运动的带电小球B恰好能沿大圆轨道运动,求带电小球A碰撞后所做圆周运动的轨道半径(设碰撞时两个带电小球间电荷量不转移)。
(1)两小球都带负电荷,
(2)两带电小球的绕行方向都相同 (3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500806613.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500790607.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500806613.png)
试题分析: (1)因为两带电小球都在复合场中做匀速圆周运动,故必有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500806594.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500837674.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500852655.png)
且
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500696560.png)
可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500790607.png)
(2)由题意可知,两带电小球的绕行方向都相同
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500915778.png)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500930693.png)
由题意有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500946556.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500962592.png)
(3)由于两带电小球在P处相碰,切向合外力为零,故两带电小球在相碰处的切向动量守恒,
有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001500993771.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001501008629.png)
而
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250015010241442.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001501055819.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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