题目内容
(18分)如图(a)所示,在以O为圆心,内外半径分别为R1和R2的圆环区域内,存在辐射状电场和垂直纸面的匀强磁场,内外圆间的电势差U为常量,R1=R0,R2=3R0,一电荷量为+q,质量为m的粒子从内圆上的A点进入该区域,不计重力。
⑴已知粒子从外圆上以速度v1射出,求粒子在A点的初速度v0的大小。
⑵若撤去电场,如图(b),已知粒子从OA延长线与外圆的交点C以速度v2射出,方向与OA延长线成45°角,求磁感应强度的大小及粒子在磁场中运动的时间。
⑶在图(b)中,若粒子从A点进入磁场,速度大小为v3,方向不确定,要使粒子一定能够从外圆射出,磁感应强度应小于多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247243335951.gif)
⑴已知粒子从外圆上以速度v1射出,求粒子在A点的初速度v0的大小。
⑵若撤去电场,如图(b),已知粒子从OA延长线与外圆的交点C以速度v2射出,方向与OA延长线成45°角,求磁感应强度的大小及粒子在磁场中运动的时间。
⑶在图(b)中,若粒子从A点进入磁场,速度大小为v3,方向不确定,要使粒子一定能够从外圆射出,磁感应强度应小于多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247243335951.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724349651.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247243804111.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247243961257.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724411575.gif)
:⑴根据动能定理,
,所以![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724349651.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247244434301.gif)
⑵如图所示,设粒子在磁场中作匀速圆周运动的半径为R,由几何知识可知
,解得:
。根据洛仑兹力公式
,解得:
。
根据公式
,
,
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247243961257.gif)
⑶考虑临界情况,如图所示
①
,解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124725004539.gif)
②
,解得:
,综合得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724411575.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724411688.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724349651.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247244434301.gif)
⑵如图所示,设粒子在磁场中作匀速圆周运动的半径为R,由几何知识可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724474475.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724536348.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724552570.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724567865.gif)
根据公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724895457.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724926454.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724552570.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247243961257.gif)
⑶考虑临界情况,如图所示
①
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724989608.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124725004539.gif)
②
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124725020636.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124725035572.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124724411575.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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