题目内容
固定在匀强磁场中的正方形导线框abcd各边长为l,其中ab是一段电阻为R的均匀电阻丝,其余三边电阻可忽略的铜线,磁感应强度为B,方向垂直纸面向里.现有一段与ab完全相同的电阻丝PQ架在导线框上(如图12-3-14所示),以恒定速度
从ad滑向bc,当PQ滑到距离ad多少时,通过PQ段电阻丝的电流最小?最小电流为多少?方向如何?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139433503864.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943334193.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139433503864.jpg)
PQ滑到ab的中点;
; 由Q到P
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943366468.gif)
根据题意画出如右图所示的等效电路图,当总电阻最大时,通过PQ段电阻丝的电流最小,
与
并联,又由于
,根据所学稳恒电流的知识得到:当
=
时外电路电阻最大,即总电阻最大.
故PQ滑到ab的中点时PQ段电阻丝的电流最小
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139434752412.jpg)
根据法拉第电磁感应定律得到产生的感应电动势为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943490288.gif)
故流过PQ电阻丝的最小电流(即总电流)为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943896904.gif)
根据右手定则得到电流方向由Q到P
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943381240.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943397241.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943397499.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943381240.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943397241.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943459619.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241139434752412.jpg)
根据法拉第电磁感应定律得到产生的感应电动势为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943490288.gif)
故流过PQ电阻丝的最小电流(即总电流)为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113943896904.gif)
根据右手定则得到电流方向由Q到P
![](http://thumb2018.1010pic.com/images/loading.gif)
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