题目内容
如图所示,Ⅰ、Ⅱ、Ⅲ为电场和磁场的理想边界,一束电子(电量为e,质量为m,重力不计)由静止状态从P点经过Ⅰ、Ⅱ间的电场加速后垂直到达边界Ⅱ的Q点。匀强磁场的磁感应强度为B,磁场边界宽度为d,电子从磁场边界Ⅲ穿出时的速度方向与电子原来的入射方向夹角为30°。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242355339233170.png)
(1)电子在磁场中运动的时间t;
(2)若改变PQ间的电势差,使电子刚好不能从边界Ⅲ射出,则此时PQ间的电势差U是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242355339233170.png)
(1)电子在磁场中运动的时间t;
(2)若改变PQ间的电势差,使电子刚好不能从边界Ⅲ射出,则此时PQ间的电势差U是多少?
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235535936746.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235534844634.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235535936746.png)
试题分析:(1)电子进入磁场后做匀速圆周运动,
设其半径为R,则 evB=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235537215581.png)
电子在磁场的周期为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235538510655.png)
于是得电子在磁场中运动周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235540008737.png)
电子在磁场中的轨迹如图,由几何关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235541505754.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242355427844320.png)
联立以上各式得电子在磁场中运动时间t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235543970633.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235545468464.png)
所以t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235534844634.png)
(2)电子刚好不从边界Ⅲ穿出时,说明电子在磁场中做匀速圆周运动的轨迹恰好与区域的右边界相切,画出电子的运动轨迹如图所示,运动半径为R=d
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242355464354328.png)
设电子在PQ间被加速电场加速后速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235547714265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235549071748.png)
电子在磁场中做匀速圆周运动,洛伦兹力提供向心力,根据牛顿第二定律得:evB=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235550678602.png)
以上三式联立解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235551895879.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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