题目内容
(14分)一根电阻R=0.6 Ω的导线弯成一个圆形线圈,圆半径r=1 m,圆形线圈质量m=1 kg,此线圈放在绝缘光滑的水平面上,在y轴右侧有垂直线圈平面的磁感应强度B=0.5 T的匀强磁场,如图15所示.若线圈以初动能E0=5 J沿x轴方向滑进磁场,当进入磁场0.5 m时,线圈中产生的电能为E=3 J.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414429944046.jpg)
(1)此时线圈的运动速度的大小;
(2)此时线圈与磁场左边缘两交接点间的电压;
(3)此时线圈加速度的大小.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241414429944046.jpg)
(1)此时线圈的运动速度的大小;
(2)此时线圈与磁场左边缘两交接点间的电压;
(3)此时线圈加速度的大小.
(1)2 m/s (2)
V (3)2.5 m/s2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443041503.png)
(1)设线圈的速度为v,由能量守恒定律得
E0=E+
mv2.
解得:v=2 m/s.
(2)线圈切割磁感线的有效长度
L=2
=
m,
电动势E=BLv=
V,
电流I=
=
A,
两交接点间的电压
U=IR1=
×0.6×
V=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443665382.png)
V.
(3)F=ma=BIL,所以a=2.5 m/s2.
E0=E+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443119338.png)
解得:v=2 m/s.
(2)线圈切割磁感线的有效长度
L=2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443213611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443291344.png)
电动势E=BLv=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443291344.png)
电流I=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443431440.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443478520.png)
两交接点间的电压
U=IR1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443478520.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443665382.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443665382.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141443291344.png)
(3)F=ma=BIL,所以a=2.5 m/s2.
![](http://thumb2018.1010pic.com/images/loading.gif)
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