题目内容
如图所示,半径为r的圆形区域内有方向垂直纸面向里的匀强磁场,圆心O1在x轴上,且OO1等于圆的半径。虚线MN平行于x轴且与圆相切,在MN的上方存在匀强电场和匀强磁场,电场强度的大小为E0,方向沿x轴的负方向,磁感应强度的大小为B0,方向垂直纸面向外。两个质量为m、电荷量为q的正粒子a、b,以相同大小的初速度从原点O射入磁场,速度的方向与x轴夹角均为30?。两个粒子射出圆形磁场后,垂直MN进入MN上方场区中恰好都做匀速直线运动。不计粒子的重力,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500413962111007.png)
(1)粒子初速度v的大小。
(2)圆形区域内磁场的磁感应强度B的大小。
(3)只撤去虚线MN上方的磁场B0,a、b两个粒子到达y轴的时间差△t 。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500413962111007.png)
(1)粒子初速度v的大小。
(2)圆形区域内磁场的磁感应强度B的大小。
(3)只撤去虚线MN上方的磁场B0,a、b两个粒子到达y轴的时间差△t 。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250041397151630.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139652639.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139699890.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250041397151630.png)
试题分析:(1)粒子进入MN上方后恰好做匀速直线运动,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139746169.png)
粒子的初速度大小
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139652639.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500413979353084.png)
(2)如图,由几何关系得粒子作圆周运动的半径R=r
由动力学知识可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139808894.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139699890.png)
(3)粒子在圆形磁场中作圆周运动的周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139840863.png)
ab两粒子在磁场中运动的时间差
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139871796.png)
由几何关系:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139886620.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139902645.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139933770.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139949750.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139964771.png)
Ab两粒子在电场中做类平抛运动的时间差
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004139996689.png)
由几何知识得,两粒子离开圆形磁场区域到进入水平匀强磁场之前做匀速直线运动,两者所用的时间相同。所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004140167687.png)
各式联立可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250041397151630.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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