一、单选题(本题共8小题,每小题4分,共32分,在每小题给出的四个选项中,只有一项是符合题目要求的,选对的得4分,选错或者不答的得0分)
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A . 大小跟速度无关
B . 可以不与速度垂直
C . 总是与磁场垂直
D . 可以不与磁场垂直
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3.
(2023高二下·北京月考)
如图,速度选择器两极板间有互相垂直的匀强电场和匀强磁场,一电荷量为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的粒子以水平速度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
从左侧射入,恰能沿直线飞出速度选择器,不计粒子重力和空气阻力。下列说法正确的是( )
![](//tikupic.21cnjy.com/2023/03/29/a5/05/a505920d81ecb849a0aca8a5922c663f_155x130.png)
A . 若仅将粒子改为从右侧射入,粒子仍将沿直线飞出
B . 若仅将粒子改为从右侧射入,粒子不能沿直线飞出
C . 若仅将电荷量改为
, 粒子不能沿直线飞出
D . 若仅将电荷量改为
, 粒子不能沿直线飞出
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4.
(2023高二下·北京月考)
如图所示的半圆形闭合回路半径为a,电阻为R。虚线MN右侧有磁感应强度为B的匀强磁场,方向垂直于半圆形回路所在的平面。回路以速度v向右匀速进入磁场,直径CD始终与MN垂直。从D点到达边界开始到C点进入磁场为止,下列结论正确的是( )
![](//tikupic.21cnjy.com/2023/03/29/1e/15/1e1511b57d58af3e82e9c7474a510146_226x196.png)
A . 感应电动势大小不变
B . 感应电动势大小一直增大
C . 感应电动势大小一直减小
D . 感应电动势最大值Bav
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5.
(2024高二下·成都期中)
某同学用粗细均匀的金属丝弯成如图所示的图形,两个正方形的边长均为L,A、B两点之间的距离远小于L,在右侧正方形区域存在均匀增强的磁场,磁感应强度随时间的变化率
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3E%CE%94%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3E%CE%94%3C%2Fmi%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 则A、B两点之间的电势差
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EU%3C%2Fmi%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
为( )
![](//tikupic.21cnjy.com/2023/03/29/e8/12/e812a5aa77b88513b3d50f9c7a1139c0_176x113.png)
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6.
(2023高二下·北京月考)
如图所示,由粗细均匀的电阻丝制成的边长为l的正方形线框abcd,其总电阻为R,现使线框以水平向右的速度v匀速穿过一宽度为2l、磁感应强度为B的匀强磁场区域,整个过程中ab、cd两边始终保持与磁场边界平行。令线框的cd边刚好与磁场左边界重合时t=0,规定电流方向沿顺时针为正,U
0=Blv。线框中电流及a、b两点间电势差U
ab随线框ad边的位移x变化的图像正确的是( )
![](//tikupic.21cnjy.com/2023/03/29/5b/8c/5b8ccd893ef37a9f0227b93378586408_213x148.png)
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7.
(2023高二下·北京月考)
如图所示,在虚线上方足够大的空间存在垂直纸面向里的匀强磁场,磁感应强度大小为B。一带正电粒子从A点以速率
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
射入磁场,速度方向与虚线的夹角
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3E%CE%B8%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E30%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 粒子经过磁场偏转后从C点射出磁场。已知A点和C点的距离为L,不计粒子的重力。则粒子的比荷
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmi%3Eq%3C%2Fmi%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
是( )
![](//tikupic.21cnjy.com/2023/03/29/19/70/1970625040284706efb1f8de150811e9_174x127.png)
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8.
(2024高二上·松原期中)
在如图所示的电路中,A
1和A
2是两个
相同的灯泡.线圈L的自感系数足够大,电阻不可以忽略。下列说法正确的是( )
![](//tikupic.21cnjy.com/2023/03/29/ae/78/ae78eb4259258f8a6cba1cf0d6f578d7_168x148.png)
A . 闭合开关S时,A1和A2同时亮
B . 闭合开关S时,A2先亮,A1逐渐变亮
C . 断开开关S后的瞬间,A2闪亮一下再熄灭
D . 断开开关S后的瞬间,流过A2的电流方向向右
二、多选题(本题共3小题,每小题6分,共18分,在每小题给出的四个选项中,有多项符合题目要求的,全部选对的得6分,选对但不全的得3分,选错或者不答的得0分)
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9.
(2023高二下·北京月考)
用一根横截面积为S、电阻率为ρ的硬质导线做成一个半径为r的圆环,ab为圆环的直径。如图所示,在ab的左侧存在一个匀强磁场,磁场垂直圆环所在平面,方向如图,磁感应强度随时间的变化规律为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(k>0),则( )
![](//tikupic.21cnjy.com/2023/03/29/b5/3e/b53ecefb7895232f1092dde08272317b_127x135.png)
A . 圆环有扩张的趋势
B . 圆环有收缩的趋势
C . 圆环有向左滑动的趋势
D . 圆环有向右滑动的趋势
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10.
(2023高二下·北京月考)
如图所示,在光滑绝缘水平面上有一单匝线圈ABCD,在水平外力作用下以大小为v的速度向右匀速进入竖直向上的匀强磁场,第二次以大小为3v的速度向右匀速进入该匀强磁场,则下列说法正确的是( )
![](//tikupic.21cnjy.com/2023/03/29/10/f1/10f1010414914f147d5bea8fa1399f41_206x113.png)
A . 第一次进入与第二次进入时线圈中的电流之比为3:1
B . 第一次进入与第二次进入时线圈中的电流之比为1:3
C . 第一次进入与第二次进入时通过线圈中某一横截面的电荷量之比为1:3
D . 第一次进入与第二次进入时通过线圈中某一横截面的电荷量之比为1:1
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三、实验题(本题共2题,12题7分,第(1)问1分,第(2)题每小空2分,13题7分,第(1)(3)题每小空1分,第(2)题每小空2分,共14分)
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(1)
下列操作中,电流表的指针不会发生偏转的是( )
A . 将条形磁铁插入线圈
B . 将条形磁铁从线圈中拔出
C . 将条形磁铁放在线圈中不动
D . 将条形磁铁从图示位置向左移动
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(2)
某实验小组将电池、线圈A、线圈B、滑动变阻器、灵敏电流计、开关按照如图所示的方式连接。当闭合开关时发现灵敏电流计的指针右偏。由此可知:
(a)当滑动变阻器的滑片P向右移动时,灵敏电流计的指针(填“左偏”、“不动”、“右偏”);(b)将线圈A拔出时,灵敏电流计的指针(填“左偏”、“不动”、“右偏”),此时线圈A与线圈B中电流的绕行方向(填“相同”或“相反”)。
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13.
(2023高二下·北京月考)
某实验小组用实验室提供的器材结合图甲电路原理图测量了一节干电池的电动势和内阻,请完成有关该实验的以下问题。
![](//tikupic.21cnjy.com/2023/02/22/6c/42/6c4207a19b26f9836fdf65cfbeffd1bd_608x246.png)
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(1)
按图甲电路原理图连接好实验器材,在开关闭合前滑动变阻器的滑片P应滑到端(“a”或“b”)。
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(2)
实验小组进行了多次实验测量,并根据实验测得的多组数据作出了U-I图像如图乙所示,由图像可确定:电源的电动势E=V,电源的内阻r=Ω(结果保到小数点后两位)。
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(3)
在处理实验数据得出实验结果后,实验小组对这种实验方案测得电动势和内电阻的实验值与真实值进行了分析,发现:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3E%E6%B5%8B%3C%2Fmi%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3E%E7%9C%9F%3C%2Fmi%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(选填“>”或“=”或“<”),
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmi%3E%E6%B5%8B%3C%2Fmi%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmi%3E%E7%9C%9F%3C%2Fmi%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(选填“>”或“=”或“<”)。
四、解答题(本题共3小题,其中13题10分,14题10分,15题16分,共36分)
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14.
(2023高二下·北京月考)
如图所示,边长为L的正方形金属框ABCD质量为m,电阻为R,用细线把它悬挂于一个有界的匀强磁场中,金属框的一半处于磁场内,磁场方向与线框平面垂直。磁场随时间变化规律为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
)。重力加速度为g。求:
![](//tikupic.21cnjy.com/2023/03/29/dc/25/dc255cfc52105f516da799bc93de899d_148x147.png)
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(3)
从
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
时刻开始,经多长时间细线的拉力为零?
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15.
(2023高二下·北京月考)
如图所示,在
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmi%3EO%3C%2Fmi%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
平面直角坐标系的第Ⅰ象限内有一垂直纸面向里的圆形匀强磁场区域,与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%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%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
轴分别相切于
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmi%3EL%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
两点,第Ⅱ象限内有沿
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
轴负方向的匀强电场。一个质量为
![](//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)
、电荷量为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmath%3E)
的带正电粒子从
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmath%3E)
点沿
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
轴正方向以
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
射入磁场,经
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
点射入电场,最后从
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴上离
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmath%3E)
点的距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3EL%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
点射出,不计粒子的重力。求:
![](//tikupic.21cnjy.com/2023/03/29/ad/68/ad68b739881aebb8b4375499dcea10e4_342x220.png)
-
(1)
匀强磁场磁感应强度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmath%3E)
的大小;
-
(2)
匀强电场场强
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
的大小;
-
16.
(2023高二下·北京月考)
如图所示,两根足够长平行金属导轨
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmi%3EN%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
、
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EQ%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
固定在倾角
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3E%CE%B8%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E37%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的绝缘斜面上,顶部接有一阻值
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3ER%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3E%CE%A9%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的定值电阻,下端开口,轨道间距
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 整个装置处于磁感应强度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3ET%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的匀强磁场中,磁场向垂直斜面向上,质量
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmtext%3Ekg%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的金属棒ab置于导轨上,ab在导轨之间的电阻
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmi%3E%CE%A9%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 电路中其余电阻不计,金属棒ab由静止释放后沿导轨运动时始终垂直于导轨,且与导轨接触良好,不计空气阻力影响。已知金属棒ab与导轨间动摩擦因数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3E%CE%BC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Esin%3C%2Fmi%3E%3Cmn%3E37%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.6%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ecos%3C%2Fmi%3E%3Cmn%3E37%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0.8%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 取
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E10%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Em%2Fs%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
。
![](//tikupic.21cnjy.com/2023/03/29/f1/2a/f12ad1c8bda3a7aca8b26c87d18c8aef_307x173.png)
-
(1)
求金属棒ab沿导轨向下运动的最大速度
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmtext%3Em%3C%2Fmtext%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
-
(2)
若从金属棒ab开始运动至达到最大速度过程中,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%3C%2Fmath%3E)
上产生的焦耳热总共为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E1.5%3C%2Fmn%3E%3Cmtext%3EJ%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 求这段过程中金属棒向下运动的位移x和流过电阻
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmath%3E)
的总电荷量q。