题目内容
如图所示,
是位于足够大的绝缘光滑水平桌面内的平面直角坐标系,虚线MN是∠
的角平分线.在MN的左侧区域,存在着沿
轴负方向、场强为E的匀强电场;在MN的右侧区域,存在着方向竖直向下、磁感应强度为B的匀强磁场,现有一带负电的小球
从y轴上的P(0,L)点,在电场力作用下由静止开始运动,小球
到达虚线MN上的Q点时与另一个不带电的静止小球
发生碰撞,碰后两小球粘合在一起进入磁场,它们穿出磁场的位置恰好在O点.若
、
两小球的质量相等且均可视为质点,
、
碰撞过程中无电荷量损失,不计重力作用.求:
(1)小球
的比荷
(即电荷量与质量之比);
(2)过O点后,粘在一起的两个小球再次到达虚线MN上的位置坐标(结果用E、B、L表示).![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241241529734499.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152786362.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152802357.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152817183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152864192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152864192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152864192.gif)
(1)小球
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152958198.gif)
(2)过O点后,粘在一起的两个小球再次到达虚线MN上的位置坐标(结果用E、B、L表示).
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241241529734499.jpg)
(1)设
的质量为
、电荷量为
,
与
碰撞前后的速度大小分别为
、
,碰后两球在磁场中运动的轨道半径为R.
在电场中做匀加速直线运动,由动能定理得:
(2分)
与
碰撞中动量守恒,有:
(2分)解得
(2分)
由题意知,Q点的位置坐标一定是(L,L),且碰后两球在磁场中做匀速圆周运动的圆心O1一定在
轴上,如图,所以R=L(2分)由洛伦兹力提供向心力有:
(2分)故有
(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241241534575283.jpg)
(2)过O点后,两球以沿
轴正方向的初速度
在电场中做类平抛运动,设它们再次到达虚线MN上的位置坐标为
,在电场中运动的时间为
由运动学公式的:
(2分)
(2分)且
(2分)解得:
,所以两球再次到达虚线MN上的位置坐标是![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153707455.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153051202.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153067199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152864192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153238205.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153254189.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153316536.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152833188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152864192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153379446.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153379550.gif)
由题意知,Q点的位置坐标一定是(L,L),且碰后两球在磁场中做匀速圆周运动的圆心O1一定在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124152817183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153426546.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153441547.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241241534575283.jpg)
(2)过O点后,两球以沿
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153472192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153254189.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153597417.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153613181.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153644547.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153660356.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153675466.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153691390.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124153707455.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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