题目内容
如图,在XOY平面第一象限整个区域分布一匀强电场,电场方向平行y轴向下.在第四象限内存在一有界匀强磁场,左边界为Y轴,右边界为
的直线,磁场方向垂直纸面向外.一质量为m、带电量为+q的粒子从y轴上P点以初速度v0垂直y轴射入匀强电场,在电场力作用下从X轴上Q点以与X轴正方向45°角进入匀强磁场.已知OQ=d,不计粒子重力.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500380459010657.png)
(1)P点坐标;
(2)要使粒子能再进入电场,磁感应强度B的取值范围;
(3)要使粒子能第二次进入磁场,磁感应强度B的取值范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003804544498.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500380459010657.png)
(1)P点坐标;
(2)要使粒子能再进入电场,磁感应强度B的取值范围;
(3)要使粒子能第二次进入磁场,磁感应强度B的取值范围.
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038050271242.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003804606607.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038048241055.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038050271242.png)
试题分析:(1)设粒子离开电场时y方向的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805183350.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805214731.png)
设粒子在电场中运动时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805230267.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805246555.png)
竖直方向匀变速,所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805261802.png)
由以上各式,解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805277610.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805292289.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003804606607.png)
(注:此问解法较多,可视具体情况给分)
(2)粒子刚好能再进入电场的轨迹如图所示,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038054333658.jpg)
设此时的轨迹半径为r1,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805448767.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805480695.png)
令粒子在磁场中的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805495265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805511674.png)
根据牛顿第二定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805542795.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038055581048.png)
要使粒子能再进入电场,磁感应强度B的范围
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038048241055.png)
(3)要使粒子刚好从
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805589593.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038056043793.jpg)
粒子从P到Q的时间为t,竖直方向速度从0增加到
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805183350.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805183350.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805183350.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805682365.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805698580.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038057291266.png)
设此时粒子在磁场中的轨道半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805745321.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805760850.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805792674.png)
根据牛顿第二定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805807823.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003805823854.png)
要使粒子能第二次进磁场,粒子必须先进入电场,故磁感应强度B要满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038048241055.png)
综上所述要使粒子能第二次进磁场,磁感应强度B要满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250038050271242.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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