题目内容
如图所示,一根粗金属棒MN固定放置,它的M一端连一个定值电阻R,定值电阻的另一端连接在金属轴O上.另外一根长为l的金属棒ab,a端与轴O相连,b端与MN棒上的一点接触,此时ab与MN间的夹角为45°角,如图所示.空间存在着方向垂直纸面向外的匀强磁场,磁感强度大小为B.现使ab棒以O为轴逆时针匀速转动一周,转动角速度大小为ω,转动过程中凡能与MN棒接触的都接触良好,两金属棒的电阻都可忽略不计.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158347422637.gif)
(1)写出电阻R中有电流存在的时间.
(2)写出这段时间内感应电流i随时间t变化的关系式.
(3)求出这段时间内流过电阻R的总电量.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158347422637.gif)
(1)写出电阻R中有电流存在的时间.
(2)写出这段时间内感应电流i随时间t变化的关系式.
(3)求出这段时间内流过电阻R的总电量.
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158347731004.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158347891051.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348041298.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348041136.gif)
(3)Bl2/2R
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348362785.gif)
(1)只在开始转动后的前T/4时间内棒ab与MN接触,因此有电流存在的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158347731004.gif)
(2)在二者接触的某时刻t,棒ab的位置如图所示,此时棒ab转过的角度为ωt.再作一条辅助线垂直于MN,即图中虚线.
此时切割磁感线的有效长度为l’=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348671243.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348821365.gif)
结论是当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158347891051.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348041298.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158348041136.gif)
(3)求流过电阻R的总电量需用电流的平均值.在前T/4时间内的感应电流的平均值
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158349451088.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241158349601405.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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