题目内容
(11分)如图11甲所示,用粗细均匀的导线制成的一只圆形金属圈,现被一根绝缘丝线悬挂在竖直平面内处于静止状态,已知金属圈的质量为m,半径为r,导线的电阻率为ρ,截面积为S.金属圈的上半部分处在一方向垂直圈面向里的有界匀强磁场中,磁感应强度B随时间t的变化满足B=kt(k为常量),如图11乙所示.金属圈下半部分在磁场外.若丝线所能承受的最大拉力FTm=2mg,求:从t=0时刻起,经过多长时间丝线会被拉断?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414375343754.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414375343754.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437550828.png)
设金属圈受重力mg、拉力FT和安培力F的作用处于静止状态,则FT=mg+F,又F=2BIr,
金属圈中的感应电流I=
,
由法拉第电磁感应定律得
E=
,
=
·
,
金属圈的电阻R=ρ
,
又B=kt,FTm=2mg
由以上各式求得t=
.
金属圈中的感应电流I=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437612440.png)
由法拉第电磁感应定律得
E=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437659508.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437659508.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437784514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437846544.png)
金属圈的电阻R=ρ
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437909581.png)
又B=kt,FTm=2mg
由以上各式求得t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141437550828.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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