15.
如图所示,间距为2d(
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ed%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
)的平行金属导轨放置在绝缘水平面上,导轨左端连一电容
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3EF%3C%2Fmtext%3E%3C%2Fmath%3E)
的电容器,初始时电容器不带电。空间分布着n个宽度为0.5d、间距为d的匀强磁场区域,从右到左依次记为区域1、区域2、区域3…,磁感应强度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmtext%3ET%3C%2Fmtext%3E%3C%2Fmath%3E)
, 方向垂直水平面向下,磁场边界与导轨垂直,且导体棒ab左侧的无磁场区域导轨表面涂有绝缘涂层。长度为d的绝缘棒将导体棒ab和边长为d的正方形单匝线框连接组成“
![](//tikupic.21cnjy.com/2024/03/24/d9/0a/d90a4ba56b31fb48569cf3c7b1aa9936.png)
”形装置,总质量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmtext%3Ek%3C%2Fmtext%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
;线框电阻
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3E%CE%A9%3C%2Fmtext%3E%3C%2Fmath%3E)
, 导体棒和导轨的电阻极小。线框右边与导体棒平行且固定在弹射器上,导体棒ab位于磁场右边界外。
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
时刻,闭合开关S,同时将“
![](//tikupic.21cnjy.com/2024/03/24/d9/0a/d90a4ba56b31fb48569cf3c7b1aa9936.png)
”形装置以速度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%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%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmrow%3E%3Cmrow%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmo%3E%2F%3C%2Fmo%3E%3Cmrow%3E%3Cmtext%3Es%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
向左弹出。导体棒在整个运动过程中始终与导轨接触并且相互垂直。(不计空气和摩擦阻力)
![](//tikupic.21cnjy.com/2024/03/24/67/d9/67d99acb7f7f90c3befb8da890844f17.png)