题目内容
分如图所示,在A点固定一正电荷,电量为Q,在离A高度为H的C处由静止释放某带同种电荷的液珠,开始运动瞬间的加速度大小恰好为重力加速度g。已知静电常量为k,两电荷均可看成点电荷,不计空气阻力。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025184111118.png)
(1)液珠的比荷;
(2)液珠速度最大时离A点的距离h;
(3)若已知在点电荷Q的电场中,某点的电势可表示成
,其中r为该点到Q的距离(选无限远的电势为零)。求液珠能到达的最高点B离A点的高度
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025184111118.png)
(1)液珠的比荷;
(2)液珠速度最大时离A点的距离h;
(3)若已知在点电荷Q的电场中,某点的电势可表示成
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518426643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518442340.png)
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518504532.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518473924.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518489554.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518504532.png)
试题分析:(1)液珠开始运动的加速度大小为g,可知液珠在C处释放时加速度方向向上,设液珠的电量为q,质量为m,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518520906.png)
解得比荷为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518473924.png)
(2)当液珠速度最大时,库仑力与重力相等,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518551835.png)
结合(1),解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518489554.png)
(3)设CB间的电势差为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518582451.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025185981136.png)
根据动能定理有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518613958.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002518504532.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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