1.
(2024高二下·杭州月考)
如图所示,由金属和绝缘部件组成的无限长光滑平行导轨,其间距为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EL%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)
, 金属导轨中间嵌有两段由绝缘材料制成的导轨M、N(图中用黑实体表示),导轨左端连有电动势
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3EV%3C%2Fmtext%3E%3C%2Fmath%3E)
的电源.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%3E1%3C%2Fmn%3E%3Cmtext%3Ek%3C%2Fmtext%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
, 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%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3E%CE%A9%3C%2Fmtext%3E%3C%2Fmath%3E)
的三根相同导体棒ab、cd和ef垂直导轨放置,其中cd用两根很长的轻质绝缘细线悬挂,刚好与导轨接触且无挤压.ghkj是一个置于金属导轨上的“
![](//tikupic.21cnjy.com/2024/06/06/22/45/2245376a1042b8cc7640657d941995aa.png)
”型导体线框,由三根导体棒组成,每根棒质量均为m,电阻均为R,长度均为L.若ef棒与线框ghkj相碰则连接成一个正方形导体框,初始时,导体棒和线框均静止在金属导轨上.导轨上方有三个方向垂直于导轨平面向下的有界匀强磁场:紧靠绝缘导轨M左侧的区域Ⅰ中有磁感应强度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3ET%3C%2Fmtext%3E%3C%2Fmath%3E)
的磁场;区域Ⅱ中有磁感应强度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的磁场,cd棒紧靠区域Ⅱ的左边界放置;紧靠绝缘导轨N右侧的区域Ⅲ中有宽度为L、磁感应强度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3ET%3C%2Fmtext%3E%3C%2Fmath%3E)
的磁场.初始时ef处于区域Ⅱ中,区域Ⅱ、Ⅲ位于绝缘导轨N两侧.导体线框gj两点紧靠区域Ⅲ的左边界,闭合开关S,ab棒启动,进入绝缘轨道M之前已做匀速运动.导体棒ab和cd相碰后结合在一起形成“联动二棒”,与导轨短暂接触后即向右上方摆起,摆起的最大高度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eh%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmath%3E)
, 到达最高点后不再下落,同时发现ef棒向右运动,进入区域Ⅲ.不计其他电阻.求:
![](//tikupic.21cnjy.com/2024/06/06/74/ed/74ed1332b2dbc84e097a5d347ac92809.png)