1.
甲辰龙年,有研究者用如图装置实现“双龙戏珠”。图中M
1M
2和N
1N
2、M
3M
4和N
3N
4组成两对平行极板,将空间分隔为I、II、III三个区域,三个区域中有垂直于纸面的匀强磁场如图甲,磁感应强度均为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmtext%3E1%3C%2Fmtext%3E%3Cmrow%3E%3Cmtext%3E18%3C%2Fmtext%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmtext%3ET%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。两发射源紧靠极板放置,每秒每个发射源分别射出10
4个垂直极板初速度大小
![](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%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmtext%3Em%2Fs%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的正或负电子。正负电子每次经过狭缝均被加速,极板电压U
MN随时间变化由如图乙。经多次加速,正负电子恰能在荧光球表面上某点相遇,并被荧光球吸收发出荧光,实现“双龙戏珠”。已知电子比荷
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1.8%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E11%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmtext%3EC%2Fkg%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 电子质量
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E10%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E31%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmtext%3Ekg%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;以两发射源连线中点O为坐标原点,平行极板向右方向为x轴正方向;荧光球半径
![](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%3Er%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3Ecm%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 球心位置在x轴上;极板N
1N
2、M
3M
4间距
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmtext%3E3cm%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。由于极板间距极小,忽略正负电子之间相互作用、过狭缝时间及正负电子穿越极板的动能损失、忽略场的边缘效应和相对论效应,计算时
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3E%CF%80%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。
(1)正负电子各由哪个发射源射出?求电压UMN的周期T;
(2)求t=0时刻发射的正负电子相遇的时刻t0和荧光球球心的位置x1;
(3)求正负电子每秒对荧光球的冲量I;
(4)以“⌒”为一“龙节”,若同(2)在不改变“龙节”情况下,沿x轴微调荧光球的球心位置,求仍能使荧光球发光的球心位置范围。
![](http://tikupic.21cnjy.com/ct20241o/fc/51/fc5105101bbf7b1d2bb653b906e43d03.png)