题目内容
(12分)如右上图,在xOy平面第一象限整个区域分布一匀强电场,电场方向平行y轴向下.在第四象限内存在一有界匀强磁场,左边界为y轴,右边界为
的直线,磁场方向垂直纸面向外.一质量为m、带电荷量为+q的粒子从y轴上P点以初速度v0垂直y轴射人匀强电场,在电场力作用下从x轴上Q点以与x轴正方向成450角进入匀强磁场.已知OQ=l,不计粒子重力.求:
(1)粒子到达Q点的速度vQ为多大?
(2)P点的纵坐标是多少?
(3)若该粒子在磁场中运动时刚好不会穿过y轴,求磁感应强度B的大小.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235415494.png)
(1)粒子到达Q点的速度vQ为多大?
(2)P点的纵坐标是多少?
(3)若该粒子在磁场中运动时刚好不会穿过y轴,求磁感应强度B的大小.
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250052354931020.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235446503.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235462438.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250052354931020.png)
试题分析:(1)Q点速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250052355091082.png)
(2)设粒子在电场中运动时间为t,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235524619.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235556746.png)
且P点有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235556504.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235571625.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250052356024402.jpg)
(3) 设此时的轨迹半径为r,由几何关系有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235618760.png)
粒子在磁场中的速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235634784.png)
根据向心力公式得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005235649870.png)
联解④⑤⑥得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250052356651119.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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