如图甲所示,M、N为竖直放置的两块正对的平行金属板,圆形虚线为与N相连且接地的圆形金属网罩(电阻不计),板M、N上正对的小孔S
1、S
2与网罩的圆心O三点共线,网罩的半径为R,网罩内存在磁感应强度大小为B、方向垂直纸面向里的匀强磁场,金属收集屏PQ上各点到O点的距离都为2R,两端点P、Q关于连线S
1O对称,屏PQ所对的圆心角θ=120°,收集屏通过阻值为r
0的电阻与大地相连,M、N间且接有如图乙所示的随时间t变化的电压,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EU%3C%2Fmi%3E%3Cmrow%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmi%3EN%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EU%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmi%3Esin%3C%2Fmi%3E%3Cmfrac%3E%3Cmi%3E%CF%80%3C%2Fmi%3E%3Cmi%3ET%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,(式中
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EU%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmsup%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,周期T已知),质量为m、电荷量为e的质子连续不断地经S
1进入M、N间的电场,接着通过S
2进入磁场。(质子通过M、N的过程中,板间电场可视为恒定,质子在S
1处的速度可视为零,整个过程中质子的重力及质子间相互作用均不计。)