题目内容
两个带电粒子的电量相同,质量之比m1∶m2=1∶4,它们以相同的初动能同时垂直于磁场方向射入到同一匀强磁场中。⑴求这两个粒子的运动半径之比、周期之比、角速度之比;⑵若质量为m1的带电粒子在磁场中转了20圈,求质量为m2的粒子在磁场中转了几圈?(粒子重力不计)
⑴
;
;
⑵![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816514622.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816467624.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816498583.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816498559.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816514622.gif)
⑴磁场力充当向心力,
,由于动能相同,
,所以![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816467624.gif)
由
,
,由角速度和周期的关系,
,得
⑵设粒子1运动的时间为t=20T1,依题意粒子2的运动时间也为t=n2T2,所以粒子2运动的圈数为
(圈)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816529523.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816561537.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816467624.gif)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816592517.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816498583.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816623434.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816498559.gif)
⑵设粒子1运动的时间为t=20T1,依题意粒子2的运动时间也为t=n2T2,所以粒子2运动的圈数为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120816514622.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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