题目内容
(2012年2月武汉调研)如图所示,在直角坐标系O-xyz中存在磁感应强度为B=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608925532.png)
,方向竖直向下的匀强磁场,在(0,0,h)处固定一电量为+q(q>0)的点电荷,在xOy平面内有一质量为m,电量为-q的微粒绕原点O沿图示方向做匀速圆周运动。若该微粒的圆周运动可以等效为环形电流,求此等效环形电流强度I。(重力加速度为g)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413260898726345.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608925532.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608956507.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082413260898726345.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609034464.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609112423.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608956507.png)
该微粒受到重力mg、洛伦兹力FB、库仑力FE三个力的作用,方向如图所示。
FB=qvB,FE=kq2/R2,v=ωr
再由几何关系 r=htanθ,R=h/cosθ,
微粒沿z轴受力平衡,FE cosθ –mg=0,
微粒在xOy平面内做匀速圆周运动,FE sinθ –FB=mω2r
联立解得:ω2+2
ω-g/h=0。
解得:ω=(
-1)
或ω="-" (
-1)
(不合题意,舍去)
微粒圆周运动周期T=2π/ω
等效电流强度,I=q/T=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609034464.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609112423.png)
。
FB=qvB,FE=kq2/R2,v=ωr
再由几何关系 r=htanθ,R=h/cosθ,
微粒沿z轴受力平衡,FE cosθ –mg=0,
微粒在xOy平面内做匀速圆周运动,FE sinθ –FB=mω2r
联立解得:ω2+2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608956507.png)
解得:ω=(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609268344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608956507.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609268344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608956507.png)
微粒圆周运动周期T=2π/ω
等效电流强度,I=q/T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609034464.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132609112423.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132608956507.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目