题目内容
(20分)如图所示为一种获得高能粒子的装置。环形区域内存在垂直纸面向外、大小可调的匀强磁场。M、N为两块中心开有小孔的极板,每当带电粒子经过M、N板时,都会被加速,加速电压均为U;每当粒子飞离电场后,M、N板间的电势差立即变为零。粒子在电场中一次次被加速,动能不断增大,而绕行半径R不变(M、N两极板间的距离远小于R)。当t=0时,质量为m、电荷量为+q的粒子静止在M板小孔处。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039119825478.png)
(1)求粒子绕行n圈回到M板时的动能En;
(2)为使粒子始终保持在圆轨道上运动,磁场必须周期性递增,求粒子绕行第n圈时磁感应强度B的大小;
(3)求粒子绕行n圈所需总时间tn。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039119825478.png)
(1)求粒子绕行n圈回到M板时的动能En;
(2)为使粒子始终保持在圆轨道上运动,磁场必须周期性递增,求粒子绕行第n圈时磁感应强度B的大小;
(3)求粒子绕行n圈所需总时间tn。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039120451521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912014660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039120291067.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039120451521.png)
试题分析:(1)粒子绕行一圈动能的增量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912076428.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912092607.png)
(2)因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912107846.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912123845.png)
可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039121381002.png)
(3)粒子做半径为R的匀速圆周运动,每一圈所用时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912154534.png)
第一圈:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912170753.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912185780.png)
第二圈:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912201785.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912216835.png)
……
第n圈的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003912232869.png)
故绕行n圈所需总时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250039122482554.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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