题目内容
如图所示,左侧为两间距d=10 cm的平行金属板,加上电压;中间用虚线框表示的正三角形内存在垂直纸面向里的匀强磁场B1,三角形底点A与下金属板平齐,AB边的中点P恰好在上金属板的右端点;三角形区域AC右侧也存在垂直纸面向里,范围足够大的匀强磁场B2.现从左端沿中心轴线方向以v0射入一个重力不计的带电微粒,微粒质量m=1.0×10-10 kg,带电荷量q=
1.0×10-4 C;带电粒子恰好从P点垂直AB边以速度v=2×105 m/s进入磁场,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500243630613125.jpg)
(1)求带电微粒的初速度v0;
(2)若带电微粒第一次垂直穿过AC,则求磁感应强度B1及第一次在B1中飞行时间;
(3)带电微粒再次经AC边回到磁场B1后,求
的取值在什么范围可以使带电微粒只能从BC边穿出?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436291165.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500243630613125.jpg)
(1)求带电微粒的初速度v0;
(2)若带电微粒第一次垂直穿过AC,则求磁感应强度B1及第一次在B1中飞行时间;
(3)带电微粒再次经AC边回到磁场B1后,求
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436322462.png)
(1)
(2)
(3) ![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436369819.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436337791.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436353863.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436369819.png)
试题分析:(1)微粒在电场中做类平抛运动
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250024363841024.png)
(2)设带电微粒由P点垂直AB射入磁场,又垂直A C穿出,
所以作以A点为圆心的圆弧,设匀速圆周运动半径为R1,根据几何关系有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250024364001151.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436415817.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436431877.png)
在磁场中飞行时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250024364471481.png)
(3)再次经AC边回到磁场B1后不从AB边穿出就一定从BC边出磁场,所以当轨迹刚好与AB边相切时,设在B2中的半径为R2。如图所示
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500243646216663.jpg)
由几何关系:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436478923.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436493792.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436525948.png)
所以只需要
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002436369819.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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