如图甲所示,正方形荧光屏
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmath%3E)
与正方形金属板相距L水平平行放置,二者的边长也为L。金属板的中心开有小孔,小孔正下方有一通电金属丝可持续发射热电子,金属丝与金属板之间加有恒定电压U。以金属板中心小孔为坐标原点,沿平行于金属板两边和垂直金属板方向建立x、y和z坐标轴,电子从金属丝发射经小孔沿z轴正方向射入磁场区域,测得电子经电场加速后经过小孔时的速度大小介于v与
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmath%3E)
之间。z轴与荧光屏的交点为s,金属板与荧光屏之间存在磁场(图中未画出),其磁感应强度沿z轴方向的分量始终为零,沿x轴和y轴方向的分量
![](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%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3Ex%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
和
![](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%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3Ey%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
随时间周期性变化规律如图乙所示,图中
![](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%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmi%3EL%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
。已知电子的质量为m、电荷量大小为e,忽略电子间的相互作用,且电子在磁场中的运动时间远小于磁场变化周期T。求:
![](http://tikupic.21cnjy.com/2023/11/08/b3/9b/b39bf95340087be1ebd8b3d35e83eea7.png)