题目内容
如图所示,在竖直平面内,光滑绝缘直杆AC与半径为R的圆周交于B、C两点,在圆心处有一固定的正点电荷,B为AC的中点,C点位于圆周的最低点。现有一质量为m、电荷量为-q、套在杆上的带负电小球从A点由 静止开始沿杆下滑。已知重力加速度为g,A点距过C点的水平面的竖直高度为3R,小球滑到B点时的速度大小为
。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017148253581.png)
(1)小球滑至C点时的速度的大小;
(2)A、B两点的电势差
;
(3)若以C点作为零电势点,试确定A点的电势。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714810508.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017148253581.png)
(1)小球滑至C点时的速度的大小;
(2)A、B两点的电势差
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714841457.png)
(3)若以C点作为零电势点,试确定A点的电势。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714888692.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714872482.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714888692.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714888692.png)
试题分析:(1)小球从 B到C 由动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017149501054.png)
小球到C点速度 vc=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001714872482.png)
(2)小球从A到B 由动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017150131236.png)
电场力做功
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001715028895.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017150441143.png)
(3)由图知B、C等电势,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017150911238.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017151061135.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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