题目内容
(12分)如图所示,在
轴上方有一竖直向下的匀强电场区域,电场强度为
。
轴下方分布有很多磁感应强度为
的条形匀强磁场区域,其宽度均为为
,相邻两磁场区域的间距为
。现将一质量为
、电荷量为
的带正电的粒子(不计重力)从
轴上的某处静止释放。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241619010098312.png)
(1)若粒子从坐标(0,
)点由静止释放,要使它经过
轴下方时,不会进入第二磁场区,
应满足什么条件?
(2)若粒子从坐标(0,
)点由静止释放,求自释放到第二次过
轴的时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859152249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859339637.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859152249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859714430.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859854542.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161900041550.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161900369693.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161900509544.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161900743310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241619010098312.png)
(1)若粒子从坐标(0,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161901196329.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859152249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161901664321.png)
(2)若粒子从坐标(0,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161901945415.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859152249.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161902475692.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161902288772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161902475692.png)
试题分析:(1)粒子经电场加速,经过
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859152249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161902849252.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161903099775.png)
之后进入下方磁场区,依据题意可知运动半径应满足:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161903224470.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161903505683.png)
由以上三式可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241619036291123.png)
(2)当粒子从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161903785556.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161903910275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161904160772.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241619043161015.png)
进入磁场的速度大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161904643316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161904846362.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161904987783.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241619051111054.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161905392168.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161905657704.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161905907168.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241619060471019.png)
根据粒子在空间运动轨迹可知,它最低能进入第二个磁场区,它在磁场区共运动时间为半个圆周运动的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161906344974.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161859152249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161906796291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161907061772.png)
所以它在无磁场区的路程
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161907327836.png)
无磁场区运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161907576695.png)
总时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824161907701981.png)
点评:该题是一道综合性较强的题,主要是考察了带电粒子在电场中的加速、偏转和在磁场的匀速圆周运动.解决此类问题常用的方法是对过程进行分段,对各个段内的运动情况进行具体分析,利用相关的知识进行解答.这要求我们要对带电粒子在电场和磁场中的运动规律要了如指掌,尤其是带电粒子在磁场中的偏转,确定轨迹的圆心是解决此类问题的关键.
![](http://thumb2018.1010pic.com/images/loading.gif)
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