题目内容
(12分)一匀强磁场分布在以O为圆心,半径为R的圆形区域内,方向与纸面垂直,如图所示,质量为m、电荷量q的带正电的质点,经电场加速后,以速度v沿半径MO方向进入磁场,沿圆弧运动到N点,然后离开磁场,∠MON=120º,质点所受重力不计,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010066058243.png)
(1)判断磁场的方向;
(2)该匀强磁场的磁感应强度B;
(3)带电质点在磁场中运动的时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010066058243.png)
(1)判断磁场的方向;
(2)该匀强磁场的磁感应强度B;
(3)带电质点在磁场中运动的时间。
(1)垂直纸面向外 (2)B=
(3)t=![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006651671.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006636745.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006651671.png)
试题分析:(1)根据左手定则,可知该磁场方向垂直纸面向外;
(2)粒子在磁场中做匀速圆周运动,设轨道半径为r,圆心为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006667337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010066835520.png)
因此:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006698773.png)
由几何关系可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006714741.png)
联立得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006729855.png)
(3)设粒子在磁场中运动的时间为t,粒子做匀速圆周运动,期周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006745782.png)
由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006761821.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006776830.png)
因此粒子在磁场中运动的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010067921104.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001006651671.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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