题目内容
如图所示,匀强电场区域和匀强磁场区域是紧邻的且宽度相等均为d,电场方向在纸平面内,而磁场方向垂直纸面向里.一带正电粒子从O点以速度v0沿垂直电场方向进入电场.在电场力的作用下发生偏转,从A点离开电场进入磁场,离开电场时带电粒子在电场方向的偏移量为d,当粒子从C点穿出磁场时速度方向与进入电场O点时的速度方向一致,不计带电粒子的重力,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241305480356158.png)
小题1:粒子从C点穿出磁场时的速度v.
小题2:电场强度和磁感应强度的比值.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241305480356158.png)
小题1:粒子从C点穿出磁场时的速度v.
小题2:电场强度和磁感应强度的比值.
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548082504.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548113574.png)
(1)粒子在电场中做类平抛运动,则
水平:
(1分) 竖直:
(2分)
解得
速度偏转角:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548285499.png)
所以飞出电场时的速度:
(2分)
粒子在磁场中做匀速圆周运动,洛伦兹力不做功,所以穿出磁场时的速度大小为:
方向:水平向右 (2分)
三、粒子在电场中运动:
(1分) ------(1)
粒子在磁场中运动轨迹如右图所示:由几何关系,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241305484105402.png)
(2分)
粒子做匀速圆周运动:
(1分)得
(2分) ----------(2)
(1)、(2)联立,解得
(1分)
水平:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548145536.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548191868.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548223477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548254766.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548285499.png)
所以飞出电场时的速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548332821.png)
粒子在磁场中做匀速圆周运动,洛伦兹力不做功,所以穿出磁场时的速度大小为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548082504.png)
三、粒子在电场中运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241305483791115.png)
粒子在磁场中运动轨迹如右图所示:由几何关系,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241305484105402.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548457938.png)
粒子做匀速圆周运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548472751.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241305485351255.png)
(1)、(2)联立,解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130548113574.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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