题目内容
在直径为d的圆形区域内存在均匀磁场、磁场方向垂直于圆面指向纸外。一电量为q、质量的m的粒子,从磁场区域的一条直径AC上的A点射入磁场,其速度大小为v0,方向与AC成α角。若此粒子恰好能打在磁场区域圆周上的D点,AD与AC的夹角为β,如图所示,求该匀强磁场的磁感应强度B的大小。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241542187686243.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241542187686243.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241542188931274.png)
试题分析:设粒子在磁场中圆周运动半径为R,其运动轨迹如图所示,O为圆心,则有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241542191434810.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824154219190836.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824154219470304.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824154219611730.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824154219673688.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824154219814790.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241542199701138.png)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241542200941555.png)
点评:对带电粒子在有界磁场中匀速圆周运动的求解,关键是画出匀速圆周运动的轨迹,利用几何知识找出圆心及相应的半径,由圆心和轨迹用几何知识确定半径是研究带电粒子在匀强磁场中做匀速圆周运动的重要方法,题目的难度在于对几何知识的应用上。
![](http://thumb2018.1010pic.com/images/loading.gif)
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