题目内容
如图所示,圆形区域内有垂直于纸面向里的匀强磁场,一个带电粒子以速度v从A点沿直径AOB方向射入磁场,经过Δt时间从C点射出磁场,OC与OB成60°角。现将带电粒子的速度变为
v,仍从A点沿原方向射入磁场,不计重力,则粒子在磁场中的运动时间变为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032481131901.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248097419.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032481131901.png)
A.![]() | B.2Δt |
C.![]() | D.![]() |
C
试题分析:粒子运动轨迹如图所示,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032481753590.jpg)
设r为圆形磁场的半径,R为粒子轨迹半径.由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248206761.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248222717.png)
由几何知识可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248237749.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248269767.png)
设圆心角为θ,粒子在磁场中运动的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248284805.png)
当粒子速度变为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248300503.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248315792.png)
故此时粒子偏转圆心角等于90°,故粒子在磁场中运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248331881.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003248347555.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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