题目内容
(10分)如图所示,a、b、c、d为4个正离子,电荷量相等均为q,同时沿图示方向进入速度选择器后,a粒子射向P1板,b粒子射向P2板,c、d两粒子通过速度选择器后,进入另一磁感应强度为B2的磁场,分别打在A1和A2两点,A1和A2两点相距Δx。已知速度选择器两板电压为U,两板距离为d,板间磁感应强度为B1
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082415170055812686.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151700667212.png)
(1)试判断a、b、c、d四粒子进入速度选择器的速度va、vb、vc、vd大小关系。(用<、>或=表示)
(2)试求出vc、vd,
(3)试判断c、d粒子的质量mc与md是否相等,若不等,求出它们的质量差Δm
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082415170055812686.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151700667212.png)
(1)试判断a、b、c、d四粒子进入速度选择器的速度va、vb、vc、vd大小关系。(用<、>或=表示)
(2)试求出vc、vd,
(3)试判断c、d粒子的质量mc与md是否相等,若不等,求出它们的质量差Δm
(1)
(2)
(3)不等,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241517012131085.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151700823561.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151700901783.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241517012131085.png)
试题分析:(1)粒子进入速度选择器,能通过速度选择器的条件是:Eq=Bvq。若速度太小则往左边偏即a粒子,若速度太大,则向右偏即b粒子。能通过速度选择器说明v=E/B。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151700823561.png)
(2)c、d不偏转,故有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151701416546.png)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151701588754.png)
得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151700901783.png)
(3)不等,mc <md
根据洛伦兹力提供向心力则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151701744761.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241517017901199.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241517018531971.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241517012131085.png)
点评:此类题型通过结合速度选择器筛选一部分合适速度的粒子进入磁场,然后利用洛伦兹力提供向心力从而找到两粒子间隔的表达式,进而解决问题
![](http://thumb2018.1010pic.com/images/loading.gif)
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