题目内容
如图甲所示,两平行金属板的板长不超过0.2 m,板间的电压u随时间t变化的图线如图乙所示,在金属板右侧有一左边界为MN、右边无界的匀强磁场,磁感应强度
,方向垂直纸面向里.现有带正电的粒子连续不断地以速度
,沿两板间的中线
平行金属板射入电场中,磁场边界MN与中线
垂直.已知带电粒子的比荷
,粒子所受的重力和粒子间的相互作用力均忽略不计.
(1)在每个粒子通过电场区域的时间内,可以把板间的电场强度看作是恒定的.试说明这种处理能够成立的理由.
(2)设
时刻射入电场的带电粒子恰能从平行金属板边缘射出,求该带电粒子射出电场时的速度大小.
(3)对于所有经过电场射入磁场的带电粒子,设其射入磁场的入射点和从磁场射出的出射点间的距离为d,试判断d的大小是否随时间而变化?若不变,证明你的结论;若变,求出d的变化范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242159258443643.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215919026508.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215920134642.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215921756351.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215921756351.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215923738904.png)
(1)在每个粒子通过电场区域的时间内,可以把板间的电场强度看作是恒定的.试说明这种处理能够成立的理由.
(2)设
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215924689442.png)
(3)对于所有经过电场射入磁场的带电粒子,设其射入磁场的入射点和从磁场射出的出射点间的距离为d,试判断d的大小是否随时间而变化?若不变,证明你的结论;若变,求出d的变化范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242159258282180.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242159258443643.jpg)
(1)带电粒子在金属板间运动时间
故t时间内金属板间的电场可以认为是恒定的.(2) ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215926717661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242159258591161.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215926717661.png)
试题分析:(1)带电粒子在金属板间运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215927497518.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215928340506.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215929073331.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215930305779.png)
故t时间内金属板间的电场可以认为是恒定的.
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215924689442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215932505533.png)
带电粒子沿两板间的中线射入电场恰从平行金属板边缘飞出电场,电场力做功
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215933800742.png)
由动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215935032952.png)
代入数据可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215936498763.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242159376532479.jpg)
(3)设某一任意时刻射出电场的粒子速率为v,速度方向与水平方向的夹角为α,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215938464617.png)
粒子在磁场中有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215939743776.png)
可得粒子进入磁场后,在磁场中做圆周运动的半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215941178694.png)
由几何关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215942520660.png)
可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824215943409970.png)
点评:本题是组合场问题,综合应用动能定理、牛顿运动定律、运动学知识以及几何知识,中等难度
![](http://thumb2018.1010pic.com/images/loading.gif)
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