题目内容
如图所示,M、N为两块带等量异种电荷的平行金属板,两板间电压可取从零到某一最大值之间的各种数值。静止的带电粒子带电量为+q,质量为m(不计重力),从点P经电场加速后,从小孔 Q进入N板右侧的匀强磁场区域,磁感应强度大小为B,方向垂直于纸面向外,CD为磁场边界上的一绝缘板,它与N板的夹角为a=45°,孔Q到板的下端C的距离为L。当M、N两板间电压取最大值时,粒子恰垂直打在CD板上。求
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029081372913.jpg)
(1)两板间电压的最大值Um;
(2)CD板上可能被粒子打中的区域的长度![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908152266.png)
(3)粒子在磁场中运动的最长时间tm。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029081372913.jpg)
(1)两板间电压的最大值Um;
(2)CD板上可能被粒子打中的区域的长度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908152266.png)
(3)粒子在磁场中运动的最长时间tm。
(1)
;(2)
;(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908215772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908183942.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908199566.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908215772.png)
试题分析:
(1)M、N两板间电压取最大值时,粒子恰垂直打在CD板上,所以圆心在C点,CH=QC=L,故半径R1="L"
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029082462704.jpg)
又因
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908261830.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908277169.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908293875.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908183942.png)
(2)设轨迹与CD板相切于K点,半径为R2,在△AKC中:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908339839.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908355700.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908371438.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908402678.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908417425.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908433523.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908464822.png)
(3)打在QE间的粒子在磁场中运动的时间最长,均为半周期:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908480814.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002908495988.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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