题目内容
如图所示,顶角θ=45°,的金属导轨 MON固定在水平面内,导轨处在方向竖直、磁感应强度为B的匀强磁场中。一根与ON垂直的导体棒在水平外力作用下以恒定速度v0沿导轨MON向左滑动,导体棒的质量为m,导轨与导体棒单位长度的电阻均匀为r。导体棒与导轨接触点的a和b,导体棒在滑动过程中始终保持与导轨良好接触。t=0时,导体棒位于顶角O处,求:
(1)t时刻流过导体棒的电流强度I和电流方向。
(2)导体棒作匀速直线运动时水平外力F的表达式。
(3)导体棒在0~t时间内产生的焦耳热Q。
(4)若在t0时刻将外力F撤去,导体棒最终在导轨上静止时的坐标x。
(1)t时刻流过导体棒的电流强度I和电流方向。
(2)导体棒作匀速直线运动时水平外力F的表达式。
(3)导体棒在0~t时间内产生的焦耳热Q。
(4)若在t0时刻将外力F撤去,导体棒最终在导轨上静止时的坐标x。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146328511692.gif)
(1)
电流方向: b→a
(2)Q=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632929245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632944457.gif)
(3) Q=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632929245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632944457.gif)
(4) x=v0t0+ d=
=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633053618.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632866489.gif)
(2)Q=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632929245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632944457.gif)
(3) Q=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632929245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632944457.gif)
(4) x=v0t0+ d=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633007409.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633053618.gif)
(1)0到t时间内,导体棒的位移: x=t
t时刻,导体棒的长度: l=x
导体棒的电动势: E=Bl v0
回路总电阻: R=(2x+
x)r
电流强度:
电流方向: b→a
(2) F=BlI=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633100522.gif)
(3)t时刻导体棒的电功率: P=I 2R
由于I恒定 R/=v0rt∝t
因此![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633116391.gif)
Q=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632929245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632944457.gif)
(4)撤去外力持,设任意时刻t导体的坐标为x,速度为v,取很短时间Δt或很短距离Δx
在t~t+时间内,由动量定理得
BIlΔt=mΔv
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633178739.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633194489.gif)
扫过的面积ΔS=
(x=v0t)
x=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633225626.gif)
设滑行距离为d,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633241523.gif)
即 d2+2v0t0d-2ΔS=0
解之 d=-v0t0+
(负值已舍去)
得 x=v0t0+ d=
=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633053618.gif)
t时刻,导体棒的长度: l=x
导体棒的电动势: E=Bl v0
回路总电阻: R=(2x+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633069246.gif)
电流强度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632866489.gif)
电流方向: b→a
(2) F=BlI=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633100522.gif)
(3)t时刻导体棒的电功率: P=I 2R
由于I恒定 R/=v0rt∝t
因此
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633116391.gif)
Q=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632929245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114632944457.gif)
(4)撤去外力持,设任意时刻t导体的坐标为x,速度为v,取很短时间Δt或很短距离Δx
| |
| ![]() |
在t~t+时间内,由动量定理得
BIlΔt=mΔv
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633178739.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633194489.gif)
扫过的面积ΔS=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633209522.gif)
x=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633225626.gif)
设滑行距离为d,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633241523.gif)
即 d2+2v0t0d-2ΔS=0
解之 d=-v0t0+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633007409.gif)
得 x=v0t0+ d=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633007409.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114633053618.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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