题目内容
用磁场可以约束带电离子的轨迹,如图示,宽d=2cm的有界匀强磁场的横向范围足够大,磁感应强度方向垂直纸面向里,B=1T。现有一束带正电的粒子从O点以v=2×106 m / s的速度沿纸面垂直边界进入磁场。粒子的电荷量q=1.6×10-19C,质量m=3.2×10-27kg。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123614968919.gif)
(1) 粒子在磁场中运动的轨道半径r和运动时间t是多大?
(2) 粒子保持原有速度,又不从磁场上边界射出,则磁感应强度最小为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123614968919.gif)
(1) 粒子在磁场中运动的轨道半径r和运动时间t是多大?
(2) 粒子保持原有速度,又不从磁场上边界射出,则磁感应强度最小为多大?
略
(1)带电粒子进入磁场后做匀速圆周运动,轨迹如图,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241236149831146.gif)
…………① 即
解得R=4×10-2 m……②
设粒子在磁场里运动轨迹对应的圆心角为θ,则
………③ 解得
由
和
……
…④
所以带电离子在磁场里的运动时间
s ………⑤
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412361512415792.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241236151391156.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241236149831146.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123614999530.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123615014477.gif)
设粒子在磁场里运动轨迹对应的圆心角为θ,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123615030483.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123615046303.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123615061531.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123615077465.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412361509272.gif)
所以带电离子在磁场里的运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123615108490.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412361512415792.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241236151391156.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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