题目内容
(10分)如图,两根足够长的金属导轨ab、cd竖直放置,导轨间距离为L,电阻不计。在导轨上端并接两个额定功率均为P、电阻均为R的小灯泡。整个系统置于匀强磁场中,磁感应强度方向与导轨所在平面垂直。现将一质量为m、电阻可以忽略的金属棒MN从图示位置由静止开始释放。金属棒下落过程中保持水平,且与导轨接触良好。已知某时刻后两灯泡保持正常发光。重力加速度为g。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029166853707.jpg)
(1)磁感应强度的大小;
(2)灯泡正常发光时导体棒的运动速率。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029166853707.jpg)
(1)磁感应强度的大小;
(2)灯泡正常发光时导体棒的运动速率。
(1)
(2) ![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916717583.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916701796.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916717583.png)
试题分析:
(1)设小灯泡的额定电流为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916732318.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916763376.png)
由题意在金属棒沿导轨竖直下落的某时刻后,小灯泡保持正常发光,流经MN中电流为
I=2
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916732318.png)
此时金属棒MN所受的重力和安培力相等,下落的速度达到最大值,有mg=BLI③
联立①②③式得
B=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916701796.png)
(2)设灯泡正常发光时,导体棒的速率为v,由电磁感应定律与欧姆定律得E=BLv⑤
E=R
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916732318.png)
联立①②④⑤⑥式得v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002916717583.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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