题目内容
质量为M,电阻为R的薄金属条制成边长为L的闭合正方形框abb´a´。如图所示,金属方框水平放在磁极的狭缝间,方框平面与磁场方向平行。设匀强磁场仅存在于相对磁极之间,其他地方的磁场忽略不计。可认为方框的aa´边和bb´边都处在磁极间,极间磁感应强度大小为B。方框从静止开始释放,其平面在下落过程中保持水平(不计空气阻力)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413313626011076.png)
(1)求方框下落的最大速度vm(设磁场区域在竖直方向足够长);
(2)当方框下落的加速度为g/2时,求方框的发热功率P;
(3)已知方框下落的时间为t时,下落的高度为h,其速度为vt(vt<vm)。求此过程中方框中产生的热量。(根据能量守恒定律)
(4)若在同一时间t内,方框内产生的热与一恒定电流I0在该框内产生的热相同,求恒定电流I0的表达式。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413313626011076.png)
(1)求方框下落的最大速度vm(设磁场区域在竖直方向足够长);
(2)当方框下落的加速度为g/2时,求方框的发热功率P;
(3)已知方框下落的时间为t时,下落的高度为h,其速度为vt(vt<vm)。求此过程中方框中产生的热量。(根据能量守恒定律)
(4)若在同一时间t内,方框内产生的热与一恒定电流I0在该框内产生的热相同,求恒定电流I0的表达式。
(1)
(2)
(3)
(4)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331364631356.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136291914.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331363381072.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136401926.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331364631356.png)
(1)方框下落速度为v时,产生的感应电动势 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136494611.png)
感应电流
方框下落过程,受到重力G及安培力F,
,方向竖直向下
,方向竖直向下
当F=G时,方框达到最大速度,即v=vm则
方框下落的最大速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136291914.png)
(2)方框下落加速度为
时,有
,则 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136915697.png)
方框的发热功率
(3)根据能量守恒定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136401926.png)
(4)
则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331371031038.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331364631356.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136494611.png)
感应电流
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136541860.png)
方框下落过程,受到重力G及安培力F,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136603524.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331366501305.png)
当F=G时,方框达到最大速度,即v=vm则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136681908.png)
方框下落的最大速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136291914.png)
(2)方框下落加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136822390.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136884861.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136915697.png)
方框的发热功率
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331363381072.png)
(3)根据能量守恒定律,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136993939.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133136401926.png)
(4)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133137071596.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331371031038.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331364631356.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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