题目内容
(10分)如图所示,在平面直角坐标系xoy中,第一象限内有一边长为L的等边三角形区域(其AO边与y轴重合、一个顶点位于坐标原点O),区域内分布着垂直纸面的匀强磁场;第二象限内分布着方向竖直向下的匀强电场。现有质量为m、电荷量为q的带正电的粒子(不计重力),以速度v垂直OC边从三角形OC边中点垂直射入磁场,并垂直y轴进入电场,最后从x轴上的某点离开电场,已知粒子飞出电场时,其速度方向OC边平行。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241533068391891.png)
(1)粒子在磁场中运动的时间;
(2)匀强电场的场强大小。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241533068391891.png)
(1)粒子在磁场中运动的时间;
(2)匀强电场的场强大小。
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307027798.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153306949630.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307027798.png)
试题分析:由题可知带电粒子运动轨迹如图,设粒子在磁场中的运动半径为r、周期为T,则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241533071515086.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307183765.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307245775.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307339502.png)
带电粒子在磁场中运动时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307401545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307479657.png)
(2)设粒子在电场中运动时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307604326.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307666820.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307791697.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307947651.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153307027798.png)
点评:此类题型考察了带电粒子在电场中类偏转,并考察了带电粒子在磁场中的偏转,其关键问题在于找出其轨迹,从而确定圆心角和线段与半径的几何关系。
![](http://thumb2018.1010pic.com/images/loading.gif)
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