题目内容
如图所示,在某空间同时存在着互相正交的匀强电场和匀强磁场,电场的方向竖直向下。一带电体a带负电荷,电量为q1,恰能静止于此空间的c点,另一带电体b也带负电荷,电量为q2,正在过a点的竖直平面内作半径为R的匀速圆周运动,结果a、b在c处碰撞并粘合在一起,试分析a、b粘合一起后的运动性质。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146274693802.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146274693802.jpg)
带电体做半径为r的匀速圆周运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627484378.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627484378.gif)
设a、b的质量分别为
和
,b的速度为
。因为带电体
处于静止状态,故有:
…①
带电体b在竖直平面内作匀速圆周运动,则重力和电场力平衡,洛仑兹力做向心力
…②,
…③
a和b碰撞时,带电体沿速度方向的合力为零,故动量守恒,由动量守恒定律可得:
…④
a、b碰撞后合在一起,总电量为
,总质量为
,仍满足
…⑤
洛仑兹力提供向心力,带电体做半径为r的匀速圆周运动:
。联立上述方程可得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627484378.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627500233.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627500236.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627515209.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627531213.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627547341.gif)
带电体b在竖直平面内作匀速圆周运动,则重力和电场力平衡,洛仑兹力做向心力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627562345.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627687390.gif)
a和b碰撞时,带电体沿速度方向的合力为零,故动量守恒,由动量守恒定律可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627703397.gif)
a、b碰撞后合在一起,总电量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627718275.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627734283.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627734457.gif)
洛仑兹力提供向心力,带电体做半径为r的匀速圆周运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627749555.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114627484378.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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