题目内容
如图所示,纸平面内O点有一离子源,不断向纸面内各个方向放出离子,已知离子速度V=5X106m/s,荷质比
=2X107C/kg。空间中存在以粒子源为圆心垂直于纸面向里半径R1=0.5m的匀强磁场B1,在这个磁场外面还存在着以粒子源为圆心垂直于纸面向外的圆环形匀强磁场B2,外径为R2,B1= B2=0.5T,(设粒子在运动过程中不相
撞,忽略重力和粒子间的相互作用)求:
(1)粒子在B1中运动时的轨道半径为多少
(2)为了使粒子不离开磁场区域,R2的最小值
(3)求粒子从O点出发再回到O点的最短时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241233234457233.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323430357.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412332343072.gif)
(1)粒子在B1中运动时的轨道半径为多少
(2)为了使粒子不离开磁场区域,R2的最小值
(3)求粒子从O点出发再回到O点的最短时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241233234457233.jpg)
(1)r=
=0.5m
(2)如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241233234766108.jpg)
因为r= R1 所以θ=60°
R2=r+2rsinθ=
m
(3)如图
T=
=2
x10-7S
t=
T=
x10-7S
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323461423.gif)
(2)如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241233234766108.jpg)
因为r= R1 所以θ=60°
R2=r+2rsinθ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323492341.gif)
(3)如图
T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323508468.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323523196.gif)
t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323523230.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123323539357.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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