题目内容
水平面上A、B、C三点固定着三个电荷量均为Q的正点电荷,将另一质量为m的带正电的小球(可视为点电荷)放置在O点,OABC恰构成一棱长为l的正四面体,如图所示。已知静电力常量为k,重力加速度为g,为使小球能静止在O点,小球所带的电荷量为( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025176469008.png)
A.
B.
C.
D.![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517724888.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025176469008.png)
A.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517646881.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517693965.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517709769.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517724888.png)
A
试题分析:对小球进行受力分析,小球受重力和A、B、C处正点电荷施加的库仑力,设θ是A、B、C处正点电荷施加的库仑力方向与竖直方向的夹角,将库仑力分解到水平方向与竖直方向,水平方向合力为零,根据竖直方向平衡条件得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517740749.png)
其中
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517755758.png)
根据几何关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517771725.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002517771989.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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