2.
如图,Ⅰ为半径为R的匀强磁场区域,圆心为O,在圆心正下方S处有一粒子发射源,均匀地向圆内各方向发射质量为m,电荷量为q,速率为v
0的带正电粒子,每秒钟共N个,其中射向O点的粒子恰好从C点射出;Ⅱ为由平行板电容器形成的匀强电场区域,上极板带正电,下极板接地,极板长度为L,极板间距为2R,场强
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmsubsup%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Eq%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;Ⅲ为宽度足够的匀强磁场区域,磁感应强度与Ⅰ相同。在Ⅲ区域的右侧竖直固定有平行板电容器,右极板带正电,左极板接地,AB为左极板上长度为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的窄缝(窄缝不影响两极板间电场),电容器两极板电压为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmsubsup%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, O、C、A三点连线过Ⅱ区域轴线,不计粒子重力,各磁场方向如图所示,重力加速度为g。
![](http://tikupic.21cnjy.com/ct20241o/37/00/370010f8505ed59670a0c4dfaac00f9c.png)