题目内容
如图所示,abcd是一个正方形的盒子,在cd边的中点有一个小孔e,盒子中存在着沿ad方向的匀强电场.一粒子源不断地从a处的小孔沿ab方向向盒内发射相同的带电粒子,粒子的初速度为v0,经电场作用后恰从e处的小孔射出.现撤去电场,在盒中加一方向垂直于纸面的匀强磁场(图中未画出),粒子仍恰好从e孔射出.(粒子的重力和粒子间的相互作用力均可忽略),则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200025861821.gif)
(1)所加磁场的方向如何?
(2)电场强度E与磁感强度B的比值为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200025861821.gif)
(1)所加磁场的方向如何?
(2)电场强度E与磁感强度B的比值为多大?
(1)磁场方向垂直于纸面向外 (2)5v0
(1)根据粒子在电场中的偏转方向,可知粒子带正电,再根据左手定则判断,磁场方向垂直于纸面向外.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200026011300.gif)
(2)设带电粒子的电量为q,质量为m,盒子的边长为L在电场中
v0t=
①
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120002648960.gif)
t2=L ②
由①②解得E=
③
粒子在磁场中做圆周运动,洛伦兹力做向心力,设轨道半径为R.则有
qvB=m
R=
④
由图中的几何关系(L-R)2+(
)2=R2 得R=
L ⑤
■
由④⑤解得B=
⑥
由③⑥得
=5v0
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200026011300.gif)
(2)设带电粒子的电量为q,质量为m,盒子的边长为L在电场中
v0t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120002632970.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120002648960.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200026641006.gif)
由①②解得E=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200026791086.gif)
粒子在磁场中做圆周运动,洛伦兹力做向心力,设轨道半径为R.则有
qvB=m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200028201016.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200028351039.gif)
由图中的几何关系(L-R)2+(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120002632970.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120002851965.gif)
■
由④⑤解得B=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200028821074.gif)
由③⑥得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120002898979.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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