题目内容
如图所示,质量为m的矩形线框MNPQ,MN边长为a,NP边长为b;MN边电阻为R1,PQ边电阻为R2,线框其余部分电阻不计。现将线框放在光滑绝缘的水平桌面上,PQ边与y轴重合。空间存在一个方向垂直桌面向下的磁场,该磁场的磁感应强度沿y轴方向均匀,沿x轴方向按规律Bx=B0(1-kx)变化,式中B0和k为已知常数且大于零。矩形线框以初速度v0从图示位置向x轴正方向平动。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304235774230.png)
小题1:在图示位置时线框中的感应电动势以及感应电流的大小和方向;
小题2:线框所受安培力的方向和安培力的表达式;
小题3:线框的最大运动距离xm;
小题4:若R1=2R2,线框运动到
过程中,电阻R1产生的焦耳热。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304235774230.png)
小题1:在图示位置时线框中的感应电动势以及感应电流的大小和方向;
小题2:线框所受安培力的方向和安培力的表达式;
小题3:线框的最大运动距离xm;
小题4:若R1=2R2,线框运动到
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130423608478.png)
小题1:方向沿NPQMN
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304236241717.png)
小题3:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304236551359.png)
小题4:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130423842700.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130423889954.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304239511108.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304239671468.png)
感应电流的方向沿NPQMN。
(2)线框受的安培力方向沿-x方向(或水平向左),
安培力大小的表达式![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304240141683.png)
(3)根据牛顿第二定律
F=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304240922272.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304241231299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304241541255.png)
矩形框的最大运动距离![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304236551359.png)
(4)由![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304241231299.png)
得
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130424310490.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304243411650.png)
电阻R1产生的焦耳热为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304243571679.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130423889954.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304239511108.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304239671468.png)
感应电流的方向沿NPQMN。
(2)线框受的安培力方向沿-x方向(或水平向左),
安培力大小的表达式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304240141683.png)
(3)根据牛顿第二定律
F=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304240922272.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304241231299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304241541255.png)
矩形框的最大运动距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304236551359.png)
(4)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304241231299.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304242941687.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130424310490.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304243411650.png)
电阻R1产生的焦耳热为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241304243571679.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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