题目内容
如图所示,大量质量为
、电量为
的带电粒子(不计重力),由静止开始经电场加速后沿水平方向从P点进入的匀强磁场,不计各粒子之间的作用力。已知磁感应强度为B,磁场的两边界线竖直且上下足够长,宽度为
。回答下列问题:
(1)加速电场的电压为
时,粒子刚好能从磁场的右边界穿过,求![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822864261.gif)
(2)若在P点加一个速度散射器(可使粒子速度方向变化,而不改变速度大小),使粒子从P点沿各个方向射入磁场,为使磁场右边界有粒子射出,加速电压至少应为多大?
(3)在有速度散射器的情况下,将加速电压调为
,则穿过磁场的粒子中,穿越磁场的最短时间为多少?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241228229263392.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822801204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822817218.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822848198.gif)
(1)加速电场的电压为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822864223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822864261.gif)
(2)若在P点加一个速度散射器(可使粒子速度方向变化,而不改变速度大小),使粒子从P点沿各个方向射入磁场,为使磁场右边界有粒子射出,加速电压至少应为多大?
(3)在有速度散射器的情况下,将加速电压调为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822879278.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241228229263392.jpg)
解:(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823004593.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241228230205819.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823067481.gif)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823082595.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823098582.gif)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823113597.gif)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823129625.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823160725.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823347528.gif)
从图中得:最短时间的圆弧对的圆心角为:
所以:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823363661.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122822957547.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823004593.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241228230205819.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823035535.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823067481.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823082595.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823098545.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823098582.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823113597.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823129625.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823160725.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823347528.gif)
从图中得:最短时间的圆弧对的圆心角为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823347307.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122823363661.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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