题目内容
(11分)如图10所示,长为L、间距为d的平行金属板间,有垂直于纸面向里的匀强磁场,磁感应强度为B,两板不带电,现有质量为m、电荷量为q的带正电粒子(重力不计),从左侧两极板的中心处以不同速率v水平射入,欲使粒子不打在板上,求粒子速率v应满足什么条件?、
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414066313759.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414066313759.jpg)
v<
或v>![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406693814.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406646682.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406693814.png)
设粒子刚好打在上极板左边缘时(如图所示).
R1=
,
又R1=
,解得v1=
.
设粒子刚好打在上极板右边缘时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414069276144.png)
由图知:R22=L2+(R2-
)2,所以R2=
,
又R2=
,解得v2=
.
综上分析,要使粒子不打在极板上,其入射速率应满足以下条件:v<
或
v>
.
R1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406740410.png)
又R1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406787608.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406646682.png)
设粒子刚好打在上极板右边缘时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414069276144.png)
由图知:R22=L2+(R2-
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406989433.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141407052681.png)
又R2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141407114622.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406693814.png)
综上分析,要使粒子不打在极板上,其入射速率应满足以下条件:v<
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406646682.png)
v>
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141406693814.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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