题目内容
(8分)如图所示,一束电子(电荷量为e)以速度v垂直射入磁感应强度为B、宽度为d的匀强磁场中,电子穿出磁场时速度方向与入射方向的夹角为
,电子的重力忽略不计,求:
(1)电子的质量m ;
(2)穿过磁场的时间t 。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319337144086.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131933682385.png)
(1)电子的质量m ;
(2)穿过磁场的时间t 。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319337144086.jpg)
(1)电子在磁场中运动,只受洛伦兹力作用,故其轨迹是圆弧的一部分,又因为F洛⊥v,故圆心在电子穿入和穿出磁场时受到洛伦兹力指向的交点上,设为 O点。
由几何知识可知,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131933729414.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131933760478.png)
r=d/sin30°=2d (1分)
又由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131933792632.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131934041731.png)
(2)由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131933729414.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131934104935.png)
由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131934135748.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319341661148.png)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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