题目内容
如图5所示,匀强磁场中磁感应强度为B,宽度为d,一电子从左边界垂直匀强磁场射入,入射方向与边界的夹角为
,已知电子的质量为m,电量为e,要使电子能从轨道的另一侧射出,求电子速度大小的范围。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145016841012.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501591200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145016841012.gif)
电子从另一侧射出的条件是速度大于![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501700636.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501700636.gif)
如图6所示,当入射速度很小时电子会在磁场中转动一段圆弧后又从同一侧射出,速率越大,轨道半径越大,当轨道与边界相切时,电子恰好不能从另一侧射出,当速率大于这个临界值时便从右边界射出,设此时的速率为
,带电粒子在磁场中作圆周运动,由几何关系得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145017932236.gif)
①
电子在磁场中运动时洛伦兹力提供向心力
,所以
②
①②联立解得
所以电子从另一侧射出的条件是速度大于
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501715205.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145017932236.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501825466.gif)
电子在磁场中运动时洛伦兹力提供向心力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501840547.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501856475.gif)
①②联立解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501871696.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114501700636.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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