题目内容
(18分)如图所示,在矩形ABCD内对角线BD以上的区域存在有平行于AD向下的匀强电场,对角线BD以下的区域存在有垂直于纸面的匀强磁场(图中未标出),矩形AD边长L,AB边长为
L。一个质量为m、电荷+q的带电粒子(不计重力)以初速度v0从A点沿AB方向进入电场,在对角线BD的中点P处进入磁场,并从DC边上的Q点垂直于DC离开磁场,试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241340363804807.jpg)
(1)电场强度的大小
(2)带电粒子经过P点时速度的大小和方向
(3)磁场的磁感应强度的大小和方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036317336.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241340363804807.jpg)
(1)电场强度的大小
(2)带电粒子经过P点时速度的大小和方向
(3)磁场的磁感应强度的大小和方向
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036505762.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036411848.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036458465.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036505762.png)
(16分)(1)(5分)带电粒子受电场力作用做类平抛运动,则
(1分)
(1分)
Eq=ma(1分)
(2分)
(2)(5分)在竖直方向上做匀变速运动,Y方向分速度为vy,则有2 a
= vy2
得vy=
=
(2分)到P点时速度为v=
(3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241340369263625.jpg)
(3)(6分)粒子在磁场中运动轨迹的圆心就在D点,则R=
BD=
L(2分)
qvB=
(2分)
(1分)
方向垂直纸面向外( 1分)
(
外)
第一个过程为类平抛运动,利用几何关系列方程求解。第二过程为在有界磁场中的匀速圆周运动。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036583677.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036614685.png)
Eq=ma(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036411848.png)
(2)(5分)在竖直方向上做匀变速运动,Y方向分速度为vy,则有2 a
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036723394.png)
得vy=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036770354.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036801448.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036879772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241340369263625.jpg)
(3)(6分)粒子在磁场中运动轨迹的圆心就在D点,则R=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036941338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134037160449.png)
qvB=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134037222589.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134037269780.png)
方向垂直纸面向外( 1分)
(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134037347819.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134037409705.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134036505762.png)
第一个过程为类平抛运动,利用几何关系列方程求解。第二过程为在有界磁场中的匀速圆周运动。
![](http://thumb2018.1010pic.com/images/loading.gif)
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