题目内容
电子(不计重力)自静止开始经M、N板间(两板间电压为u)的电场加速后从A点垂直于磁场边界射入宽度为
L的匀强磁场中,电子离开磁场时的位置P偏离入射方向的距离为L,如图所示..(已知电子的质量为m,电量为e)求:
(1)电子在加速电场中加速后获得的速度
(2)匀强磁场的磁感应强度
(3)电子在磁场中的运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241300384223989.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038390337.png)
(1)电子在加速电场中加速后获得的速度
(2)匀强磁场的磁感应强度
(3)电子在磁场中的运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241300384223989.png)
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038500876.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038453719.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038468760.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038500876.png)
(1)电子在M、N间加速后获得的速度为v,由动能定理得:
mv2-0="eu " 解得
①
(2)电子进入磁场后做匀速圆周运动,设其半径为r,
则:evB=mv2/r②
电子在磁场中的轨迹如图,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241300387962323.png)
由几何关系得:(r-L)2+ (
L)2=r2 ③
由①②③解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038468760.png)
(3) 电子在磁场的周期为T=
,由几何关系得 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130039233674.png)
可得电子在磁场中的运动时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038500876.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038546338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038453719.png)
(2)电子进入磁场后做匀速圆周运动,设其半径为r,
则:evB=mv2/r②
电子在磁场中的轨迹如图,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241300387962323.png)
由几何关系得:(r-L)2+ (
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038968311.png)
由①②③解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038468760.png)
(3) 电子在磁场的周期为T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130039202543.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130039233674.png)
可得电子在磁场中的运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130038500876.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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