阿尔法磁谱仪(简称AMS)是美籍华裔物理学家丁肇中构思,由中国参与建造的探测反物质和暗物质的仪器。图甲是AMS在空间站的实验场景,其工作原理可简化为如图乙所示:在xOy平面内,以
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E++%EF%BC%8C+%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
为圆心、R为半径的圆形区域内有垂直纸面向里的匀强磁场,在
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
的区域内有垂直纸面向外的匀强磁场,两区域磁场的磁感应强度大小相等。在第一象限有与x轴成
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmath%3E)
角倾斜放置的接收器与x、y轴交于Q、P两点,且OQ间距为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmath%3E)
, 在圆形磁场区域左侧
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
的区域内,均匀分布着质量为m、电荷量为e的一簇质子,所有质子均以速度v沿x轴正向射入圆形磁场区域,其中正对M点射入的质子经偏转后从O点进入x轴上方的磁场。不计质子的重力,不考虑质子间的相互作用。求:
![](http://tikupic.21cnjy.com/2024/03/20/96/21/96215cf1440dba0e553483d14c0414b8.png)
图甲 图乙