题目内容
如图所示,MN为两个匀强磁场的分界面,两磁场的磁感应强度大小为B1=2B,B2=B。一电荷量为+q、质量为m的粒子从O点垂直MN进入磁感应强度为B1的磁场,则经过____________时间它将向下再一次通过O点,这段时间内粒子的平均速度为_________。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241232393282114.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241232393282114.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239344608.png)
粒子垂直进入磁场,做匀速圆周运动,半径
,则粒子在两个磁场中半径之比为1:2,画出轨迹,根据周期求出时间.
粒子垂直进入磁场,由洛伦兹力提供向心力,则根据牛顿第二定律得
得 轨迹半径
,周期
可知r1:r2=1:2 画出轨迹如图.![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241232394844570.png)
粒子在磁场B1中运动时间为T1,在磁场B2中运动时间为
,粒子向下再一次通过O点所经历时间
,位移为0,平均速度为0.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239391585.png)
粒子垂直进入磁场,由洛伦兹力提供向心力,则根据牛顿第二定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239406691.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239391585.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239453720.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241232394844570.png)
粒子在磁场B1中运动时间为T1,在磁场B2中运动时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239500494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123239516980.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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