题目内容
(14分)如图所示,竖直平面内有相互垂直的匀强电场和匀强磁场,电场强度E1=2500 N/C,方向竖直向上;磁感应强度B=103T,方向垂直纸面向外;有一质量m=1×10-2kg、电荷量q=4×10-5C的带正电小球自O点沿与水平线成45°角以v0=4 m/s的速度射入复合场中,之后小球恰好从P点进入电场强度E2=2500 N/C,方向水平向左的第二个匀强电场中.不计空气阻力,g取10 m/s2.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241615356343865.jpg)
(1)O点到P点的距离s1;
(2)带电小球经过P点的正下方Q点时与P点的距离s2.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241615356343865.jpg)
(1)O点到P点的距离s1;
(2)带电小球经过P点的正下方Q点时与P点的距离s2.
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161536009591.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161535743560.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161536009591.png)
试题分析:分析:(1)粒子在复合场中电场力和重力平衡,则只在洛仑兹力的作用下做匀速圆周运动,由牛顿第二定律可知粒子的半径,由几何关系可得出两点间的距离;
(2)粒子在电场中,由于重力和电场力的作用做类平抛运动,建立合适的坐标系,则可由运动的合成与分解求得两点间的距离.
解:(1)带电小球在正交的匀强电场和匀强磁场中受到重力G=mg=0.1N;
电场力F1=Eq=0.1N
即G=F1,故小球在正交的电场由A到C做匀速圆周运动.
根据牛顿第二定律可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161536430764.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161536601717.png)
由几何关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161536945668.png)
(2)带电小球在C点的速度大小仍为v0=4m/s,方向与水平方向成45°.
由于电场力F2=Eq=0.1N
与重力大小相等,方向相互垂直,
则合力的大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161537132612.png)
建立如图所示的坐标系,沿y方向上,小球的加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161537428851.png)
位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161537631608.png)
x方向上有小球的位移x=v0t
由几何关系可知:y=x
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161537896660.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161538161556.png)
由几何关系可知,Q到P点的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161538458701.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082416153870711794.jpg)
点评:本题考查带电粒子在复合场中的运动,要注意当粒子在复合场中做匀速圆周运动时,粒子受到的电场力与重力平衡.
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目