题目内容
(20分)如图,在直角坐标系xOy平面内,虚线MN平行于y轴,N点坐标(-l,0),MN与y轴之间有沿y轴正方向的匀强电场,在第四象限的某区域有方向垂直于坐标平面的圆形有界匀强磁场(图中未画出)。现有一质量为m、电荷量为e的电子,从虚线MN上的P点,以平行于x轴正方向的初速度v0射人电场,并从y轴上A点(0,0.5l)射出电场,射出时速度方向与y轴负方向成30°角,此后,电子做匀速直线运动,进人磁场并从圆形有界磁场边界上Q点(
l/6,-l)射出,速度沿x轴负方向。不计电子重力。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250047455353296.png)
(1)匀强电场的电场强度E的大小?
(2)匀强磁场的磁感应强度B的大小?电子在磁场中运动的时间t是多少?
(3)圆形有界匀强磁场区域的最小面积S是多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745489294.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250047455353296.png)
(1)匀强电场的电场强度E的大小?
(2)匀强磁场的磁感应强度B的大小?电子在磁场中运动的时间t是多少?
(3)圆形有界匀强磁场区域的最小面积S是多大?
(1)
(2)
,t=
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745598600.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745551810.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745567719.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745582580.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745598600.png)
试题分析:(1)设电子在电场中运动的加速度为a,时间为t,离开电场时,沿y轴方向的速度大小为vy,则a=eE/m,vy=at,l=v0t,vy=v0cot30°
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745551810.png)
(2)设轨迹与x轴的交点为D,OD距离为xD,则xD=0.5ltan30°;xD=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745645456.png)
所以,DQ平行于y轴,电子在磁场中做匀速圆周运动的轨道的圆心在DQ上,电子运动轨迹如图所示。设电子离开电场时速度为v,在磁场中做匀速圆周运动的轨道半径为r,则v0=vsin30°
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250047456604360.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745676787.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745707705.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745723445.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745738476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745754638.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745769812.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745567719.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745582580.png)
(3)以切点F、Q为直径的圆形有界匀强磁场区域的半径最小,设为r1,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250047458161031.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004745832699.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目