如图甲,粗糙绝缘水平面上有两个完全相同的金属小滑块A、B,质量均为m。空间有场强大小均为E、方向均沿水平且相反的两个匀强电场,滑块B处于电场分界线上。开始时,A带电量为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmath%3E)
, B不带电,A、B相距s,速度均为0,一段时间后A、B发生弹性正碰,且碰撞时间极短,碰后A、B所带电荷量均恒为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmath%3E)
, 碰后A的最大速度恰好与碰前的最大速度大小相等,A的部分
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmath%3E)
关系如图乙所示(
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
为未知量),整个过程中,A、B之间的库仑力视为真空中点电荷的相互作用,静电力常量为k,A、B与水平面间的最大静摩擦力等于滑动摩擦力且大小均为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eq%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
。求:
![](http://tikupic.21cnjy.com/2023/10/18/2e/67/2e6741d0f1f49918cd63d0f2947781b5_609x175.png)