题目内容
(8分)在真空室内取坐标系xOy,在x轴上方存在两个方向都垂直于纸面向外的磁场区Ⅰ和II(如图),平行于x轴的虚线MM’和NN’是它们的边界线,两个区域在y方向上的宽度都为d、在x方向上都足够长.Ⅰ区和II区内分别充满磁感应强度为B和
的匀强磁场.一带正电的粒子质量为m、电荷量为q,从坐标原点O以大小为v的速度沿y轴正方向射入Ⅰ区的磁场中.不计粒子的重力作用.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500354813728879.jpg)
(1)如果粒子只是在Ⅰ区内运动而没有到达II区,那么粒子的速度v满足什么条件?粒子运动了多长时间到达x轴?
(2)如果粒子运动过程经过II区而且最后还是从x轴离开磁场,那么粒子的速度v又满足什么条件?并求这种情况下粒子到达x轴的坐标范围?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548106497.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500354813728879.jpg)
(1)如果粒子只是在Ⅰ区内运动而没有到达II区,那么粒子的速度v满足什么条件?粒子运动了多长时间到达x轴?
(2)如果粒子运动过程经过II区而且最后还是从x轴离开磁场,那么粒子的速度v又满足什么条件?并求这种情况下粒子到达x轴的坐标范围?
(1)
(2)
,![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548215769.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548153730.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548184702.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548199968.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548215769.png)
试题分析:(1)(6分)粒子刚好没有到达Ⅱ区的轨迹如图(图1分)
由R=d 及
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548246761.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548262717.png)
即粒子只是在Ⅰ区内运动,粒子的速度v应满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548153730.png)
又根据
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548293655.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548324496.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548184702.png)
(2)(7分)粒子经过Ⅱ区而且刚好能从x轴离开磁场的轨迹如图(图1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500354835526316.jpg)
依题意,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548387790.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548402960.png)
由几何关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548418742.png)
整理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548449810.png)
设此时粒子离开磁场的坐标为L,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035484801162.png)
联立⑥⑦⑨,整理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548636630.png)
故粒子速度应满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548199968.png)
粒子到达x轴的坐标范围为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003548215769.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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