17.
(2023高二下·泸西期末)
如图所示,平行光滑金属导轨
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EQ%3C%2Fmi%3E%3Cmtext%3E%E3%80%81%3C%2Fmtext%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmi%3EN%3C%2Fmi%3E%3C%2Fmath%3E)
分别由一段圆弧和水平部分组成,水平部分固定在绝缘水平面上,导轨间距为
L ,
M、
P间接有阻值为
R的定值电阻,导轨水平部分在
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmtext%3E%E3%80%81%3C%2Fmtext%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
间有垂直导轨平面向上的匀强磁场Ⅰ,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%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EG%3C%2Fmi%3E%3Cmi%3EH%3C%2Fmi%3E%3C%2Fmath%3E)
右侧有垂直导轨平面向下的匀强磁场Ⅱ,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%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
, 金属棒
b垂直导轨放在导轨的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmtext%3E%E3%80%81%3C%2Fmtext%3E%3Cmi%3EG%3C%2Fmi%3E%3Cmi%3EH%3C%2Fmi%3E%3C%2Fmath%3E)
之间,金属棒
a在圆弧导轨上离水平面高
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eh%3C%2Fmi%3E%3C%2Fmath%3E)
处由静止释放,金属棒在导轨上运动过程中始终与导轨接触良好并与导轨垂直,两金属棒接入电路的电阻均为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmath%3E)
, 质量均为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmtext%3E%E3%80%81%3C%2Fmtext%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
间的距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Eh%3C%2Fmi%3E%3C%2Fmath%3E)
, 重力加速度为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3C%2Fmath%3E)
, 金属棒
a与
b碰撞后粘在一起,最后金属棒
a、
b停在磁场Ⅱ区域内,求:
![](//tikupic.21cnjy.com/2023/08/17/12/0b/120b692fe8b5ddba3fc1dea2266d0bbc_445x132.png)