题目内容
如图所示,在一底边长为2L,θ=45°的等腰三角形区域内(O为底边中点)有垂直纸面向外的匀强磁场. 现有一质量为m,电量为q的带正电粒子从静止开始经过电势差为U的电场加速后,从O点垂直于AB进入磁场,不计重力与空气阻力的影响。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241712545205865.jpg)
(1)粒子经电场加速射入磁场时的速度?
(2)磁感应强度B为多少时,粒子能以最大的圆周半径偏转后打到OA板?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241712545205865.jpg)
(1)粒子经电场加速射入磁场时的速度?
(2)磁感应强度B为多少时,粒子能以最大的圆周半径偏转后打到OA板?
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241712549721022.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824171254535721.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241712549721022.png)
试题分析:(1)依题意,设粒子经电场加速射入磁场时的速度为v,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824171255440793.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824171255893797.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241712561735142.jpg)
(2)要使圆周运动半径最大,则粒子的圆周运动轨迹应与AC边相切,如图所示。
,设圆周半径为R,由图中几何关系:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824171256205692.png)
由洛仑兹力提供向心力:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824171256470778.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241712568911106.png)
点评:此类问题的关键是准确的画出粒子运动的轨迹图,利用几何知识求出粒子运动的半径,再结合半径公式和周期公式去分析求解.
![](http://thumb2018.1010pic.com/images/loading.gif)
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