题目内容
如图所示,相距2L的AB、CD两直线间存在着两个大小不同、方向相反的有界匀强电场,其中PT上方的电场E1方向竖直向下,PT下方的电场E0方向竖直向上,在电场左边界AB上宽为L的PQ区域内,连续分布着电荷量为+q、质量为m的粒子。从某时刻起由Q到P点间的带电粒子,依次以相同的初速度v0沿水平方向垂直射入匀强电场E0中,若从Q点射入的粒子,通过PT上的某点R进入匀强电场E1后从CD边上的M点水平射出,其轨迹如图所示,测得MT两点的距离为L/2。不计粒子重力及它们间的相互作用。试求:(m、q、L,、a、 v0为已知量)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314350985224.jpg)
小题1:电场强度E0的大小;
小题2:在PQ间还有许多水平射入电场的粒子通过电场后也能垂直CD边水平射出,这些入射点到P点的距离有什么规律?
小题3:有一边长为a、由光滑绝缘壁围成的正方形容器,在其边界正中央开有一小孔S,将其置于CD右侧,若从Q点射入的粒子经AB、CD间的电场从S孔水平射入容器中。欲使粒子在容器中与器壁多次垂直碰撞后仍能从S孔射出(粒子与绝缘壁碰撞时无能量和电量损失),并返回Q点,在容器中现加上一个如图所示的匀强磁场,粒子运动的半径小于a,磁感应强度B的大小还应满足什么条件?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314350985224.jpg)
小题1:电场强度E0的大小;
小题2:在PQ间还有许多水平射入电场的粒子通过电场后也能垂直CD边水平射出,这些入射点到P点的距离有什么规律?
小题3:有一边长为a、由光滑绝缘壁围成的正方形容器,在其边界正中央开有一小孔S,将其置于CD右侧,若从Q点射入的粒子经AB、CD间的电场从S孔水平射入容器中。欲使粒子在容器中与器壁多次垂直碰撞后仍能从S孔射出(粒子与绝缘壁碰撞时无能量和电量损失),并返回Q点,在容器中现加上一个如图所示的匀强磁场,粒子运动的半径小于a,磁感应强度B的大小还应满足什么条件?
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314351291073.png)
小题2:y=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435160608.png)
小题3:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314352071029.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435238868.png)
(1)E0=
(2)y=
(n=1、2、3、、、、)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435488179.png)
(3)欲使粒子仍能从S孔处射出,粒子的运动轨迹可能是如图甲、乙所示的两种情况。对图甲所示的情形,粒子运动的半径为
,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314355351280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435566942.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435644794.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314356911147.png)
对图乙所示的情形,粒子运动的半径为
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435784903.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314358161371.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131436003809.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314360341038.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435238868.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314351291073.png)
(2)y=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435160608.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435488179.png)
(3)欲使粒子仍能从S孔处射出,粒子的运动轨迹可能是如图甲、乙所示的两种情况。对图甲所示的情形,粒子运动的半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435504354.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314355351280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435566942.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435644794.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314356911147.png)
对图乙所示的情形,粒子运动的半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435769360.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435784903.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314358161371.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131436003809.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314360341038.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241314352071029.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131435238868.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目