题目内容
如图14甲所示,光滑的平行水平金属导轨
、
相距
,
在
点和
点间连接一个阻值为
的电阻,在两导轨间
矩形区域内有垂直导轨平面竖直向上、宽为
的匀强磁场,磁感应强度为
。一质量为
、电阻为
、长度也刚好为
的导体棒
垂直搁在导轨上,与磁场左边界相距
。现用一个水平向右的力
拉棒
,使它由静止开始运动,棒
离开磁场前已做匀速直线运动,棒
与导轨始终保持良好接触,导轨电阻不计,
随
与初始位置的距离
变化的情况如图14乙,
已知。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412365376513231.jpg)
(1)棒
离开磁场右边界时的速度;
(2)棒
通过磁场区域的过程中整个回路所消耗的电能;
(3)
满足什么条件时,棒
进入磁场后一直做匀速运动。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653406368.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653422251.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653437197.gif)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653453327.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653484202.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653500204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653515273.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653531198.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653546206.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653546204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653562185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653437197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653609218.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653624200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653624200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653718187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653734219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412365376513231.jpg)
(1)棒
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
(2)棒
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653609218.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
解:(1)设离开右边界时棒
速度为
,则有
对棒有:
解得:
(2)在
棒运动的整个过程中,由能量守恒定律得:
解得:
(3)棒
刚进入磁场时即匀速运动,则: ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654295571.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654108185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654155302.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654170450.gif)
对棒有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654186383.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654217651.gif)
(2)在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654248764.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241236542641015.gif)
(3)棒
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123653593223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654295571.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123654311749.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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