题目内容
如图所示,带电平行金属板相距为2R,在两板间半径为R的圆形区域内有垂直纸面向里的匀强磁场,磁感应强度为B,两板及其左侧边缘连线均与磁场边界刚好相切。一质子(不计重力)沿两板间中心线O1O2从左侧O1点以某一速度射入,沿直线通过圆形磁场区域,然后恰好从极板边缘飞出,在极板间运动时间为t0。若仅撤去磁场,质子仍从O1点以相同速度射入,经
时间打到极板上。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241327020746591.png)
⑴求两极板间电压U;
⑵求质子从极板间飞出时的速度大小;
⑶若两极板不带电,保持磁场不变,质子仍沿中心线O1 O2从O1点射入,欲使质子从两板左侧间飞出,射入的速度应满足什么条件?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702012385.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241327020746591.png)
⑴求两极板间电压U;
⑵求质子从极板间飞出时的速度大小;
⑶若两极板不带电,保持磁场不变,质子仍沿中心线O1 O2从O1点射入,欲使质子从两板左侧间飞出,射入的速度应满足什么条件?
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702339861.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702136688.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702183661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702339861.png)
(1)设质子从左侧O1点射入的速度为
,极板长为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702417279.png)
在复合场中作匀速运动:
(2分)
在电场中作类平抛运动:
(2分)
又
(1分)
撤去磁场,仅受电场力,有:
(1分)
解得
(2分)
(2)质子从极板间飞出时的沿电场方向分速度大小![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702854375.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702901618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702932164.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702948480.png)
(1分)
从极板间飞出时的速度大小![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703119808.png)
(1分)
(3)设质子在磁场中做圆周运动的轨道半径为r,质子恰好从上极板左边缘飞出时速度的
偏转角为
,由几何关系可知:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703322352.png)
,r+
r=R (2分)
因为
,所以
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241327038996966.png)
根据向心力公式
,解得 v=
(2分)
所以,质子从两板左侧间飞出的条件为
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702386323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702417279.png)
在复合场中作匀速运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702542826.png)
在电场中作类平抛运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702589617.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702620843.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702651486.png)
撤去磁场,仅受电场力,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702682985.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702714492.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702729435.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702760609.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702136688.png)
(2)质子从极板间飞出时的沿电场方向分速度大小
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702854375.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702901618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702932164.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702948480.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702979338.png)
从极板间飞出时的速度大小
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703119808.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702183661.png)
(3)设质子在磁场中做圆周运动的轨道半径为r,质子恰好从上极板左边缘飞出时速度的
偏转角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703291285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703322352.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703369565.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703431320.png)
因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702682985.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241327037591078.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241327038996966.png)
根据向心力公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703930724.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132703977785.png)
所以,质子从两板左侧间飞出的条件为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132702339861.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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