题目内容
(18分)如图,静止于A处的离子,经加速电场加速后沿图中圆弧虚线通过静电分析器,从P点垂直CN进入矩形区域的有界匀强电场,电场方向水平向左。静电分析器通道内有均匀辐射分布的电场,已知圆弧虚线的半径为R,其所在处场强为E、方向如图所示;离子质量为m、电荷量为q;
、
,离子重力不计。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250048200276782.jpg)
(1)求加速电场的电压U;
(2)若离子恰好能打在Q点上,求矩形区域QNCD内匀强电场场强E0的值;
(3)若撤去矩形区域QNCD内的匀强电场,换为垂直纸面向里的匀强磁场,要求离子能最终打在QN上,求磁场磁感应强度B的取值范围。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004819965658.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004819996607.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250048200276782.jpg)
(1)求加速电场的电压U;
(2)若离子恰好能打在Q点上,求矩形区域QNCD内匀强电场场强E0的值;
(3)若撤去矩形区域QNCD内的匀强电场,换为垂直纸面向里的匀强磁场,要求离子能最终打在QN上,求磁场磁感应强度B的取值范围。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250048200741542.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820043548.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820058670.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250048200741542.png)
试题分析:(1)离子在加速电场中加速,根据动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820089860.png)
离子辐射向电场中做匀速圆周运动,由牛顿定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820105871.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820121657.png)
(2)离子做类平抛运动:2d=vt,2d=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820136543.png)
由牛顿第二定律得 qE0 = ma 则E0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820058670.png)
(3)离子在匀强磁场中做匀速圆周运动,洛伦兹力提供向心力,根据牛顿第二定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820167794.png)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820183902.png)
离子能打在QF上,则既没有从DQ边出去也没有从PF边出去,则离子运动径迹的边界如图中Ⅰ和Ⅱ。
由几何关系可知,离子能打到QF上,必须满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004820214765.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250048202301532.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250048202456810.jpg)
![](http://thumb2018.1010pic.com/images/loading.gif)
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