题目内容
如图所示,在一平面直角坐标系所确定的平面内存在着两个匀强磁场区域,以一、三象限角平分线为界,分界线为MN.MN上方区域存在匀强磁场B1,垂直纸面向里,下方区城存在匀强磁场B2,也垂直纸面向里,且有B2 =2B1=0.2T,x正半轴与ON之间的区域没有磁场。在边界线MN上有坐标为(2、2)的一粒子发射源S,不断向Y轴负方向发射各种速率的带电粒子.所有粒子带电量均为-q,质量均为m(重力不计),其荷质比为
c/kg。试问:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344216134166.png)
(1) 若S发射了两颗粒子,它们的速度分别为
m/s和
m/s,结果,经过一段时间,两颗粒子先后经过分界线ON上的点P(P未画出),求SP的距离。
(2) 若S发射了一速度为
m/s的带电粒子,经过一段时间,其第一次经过分界线MO上的点Q(Q未画出),求Q点的坐标。
(3) 若S发射了一速度为
m/s的带电粒子,求其从发出到第三次经过x轴所花费的时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421519357.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344216134166.png)
(1) 若S发射了两颗粒子,它们的速度分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421644355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421675454.png)
(2) 若S发射了一速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421863479.png)
(3) 若S发射了一速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421909475.png)
(1)SP=0(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421956899.png)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344220031669.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421956899.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344220031669.png)
(1)如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344220655643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422097550.png)
所以能回到S
所以SP=0
(2)
如图,圆心O’
设
在
中![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422253825.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422284640.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421956899.png)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422362609.png)
圆心为0,如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344224716946.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344220031669.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344220655643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422097550.png)
所以能回到S
所以SP=0
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422128932.png)
设
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422175472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422206444.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422253825.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422284640.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134421956899.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422362609.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134422393195.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344224716946.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241344220031669.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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