1.
(2023高二上·佛山)
如图,两条相距
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3El%3C%2Fmi%3E%3C%2Fmath%3E)
、电阻不计的光滑平行金属导轨位于水平面
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
纸面
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
内,其左端接一阻值为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3ER%3C%2Fmi%3E%3C%2Fmath%3E)
的电阻。一金属棒垂直置于两导轨上,接入电路部分的电阻为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Er%3C%2Fmi%3E%3C%2Fmath%3E)
;在导轨和金属棒中间有一面积为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3ES%3C%2Fmi%3E%3C%2Fmath%3E)
的区域,区域中存在垂直于纸面向里的均匀磁场,磁感应强度大小
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
随时间
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Et%3C%2Fmi%3E%3C%2Fmath%3E)
的变化关系为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%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%3Cmi+mathvariant%3D%22normal%22%3Ek%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3Et%3C%2Fmi%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi+mathvariant%3D%22normal%22%3Ek%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
, 式中
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3Ek%3C%2Fmi%3E%3C%2Fmath%3E)
为常量;在金属棒右侧有一匀强磁场,左边界
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EM%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EN%3C%2Fmi%3E%3Cmo%3E%28%3C%2Fmo%3E%3C%2Fmath%3E)
虚线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmath%3E)
与导轨垂直,磁感应强度大小为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EB%3C%2Fmi%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3C%2Fmath%3E)
方向垂直于纸面向里。某时刻,金属棒在一外加水平恒力的作用下从静止开始向右运动,在
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
时刻恰好以速度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22normal%22%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
越过
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi+mathvariant%3D%22normal%22%3EM%3C%2Fmi%3E%3Cmi+mathvariant%3D%22normal%22%3EN%3C%2Fmi%3E%3C%2Fmath%3E)
, 此后向右做匀速运动,金属棒与导轨始终相互垂直并接触良好。求:
![](//tikupic.21cnjy.com/2023/12/23/54/12/54128700f2fd9250ff18d9f310445c3e_245x172.png)