题目内容
(16分)如图,两根相距l=1m平行光滑长金属导轨电阻不计,被固定在绝缘水平面上,两导轨左端接有R=2Ω的电阻,导轨所在区域内加上与导轨垂直、方向相反的磁场,磁场宽度d相同且为0.6m,磁感应强度大小B1=
T、B2=0.8T。现有电阻r=1Ω的导体棒ab垂直导轨放置且接触良好,当导体棒ab以
m/s从边界MN进入磁场后始终作匀速运动,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026159447956.png)
⑴导体棒ab进入磁场B1时拉力的功率;
⑵导体棒ab经过任意一个B2区域过程中通过电阻R的电量;
⑶导体棒ab匀速运动过程中电阻R两端的电压有效值。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002615912439.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002615944354.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026159447956.png)
⑴导体棒ab进入磁场B1时拉力的功率;
⑵导体棒ab经过任意一个B2区域过程中通过电阻R的电量;
⑶导体棒ab匀速运动过程中电阻R两端的电压有效值。
(1)
(2)q=0.16C (3)2V
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002615959673.png)
试题分析:(1)在B1中时,根据法拉第电磁感应定律可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002615975600.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002615990635.png)
由ab做匀速运动知:拉力等于安培力即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616006561.png)
所以拉力的功率:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616037803.png)
(2)根据电荷量
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616053584.png)
再根据闭合电路的欧姆定理知
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616068775.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616084640.png)
代入解得:q=0.16C
(3)导体棒进入B2时,电动势
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616100755.png)
设电动势有效值为E,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026161151097.png)
解得:E=3V
电阻R两端电压的有效值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002616131916.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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