题目内容
如图所示,两块平行金属极板心MN水平放置,板长L="1" m,间距
,两金属板间电压
;在平行金属板右侧依次存在ABC和FGH两个全等的正三角形区域,正三角形ABC内存在垂直纸面向里的匀强磁场Bl,三角形的上顶点A与上金属板M平齐,BC边与金属板平行,AB边的中点P恰好在下金属板N的右端点;正三角形FGH内存在垂直纸面向外的匀强磁场B2,已知A、F、G处于同一直线上,B、C、H也处于同一直线上,AF两点距离为
。现从平行金属极板MN左端沿中轴线方向入射一个重力不计的带电粒子,粒子质量
,带电量
,初速度
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028288409360.jpg)
(1)求带电粒子从电场中射出时的速度v的大小和方向
(2)若带电粒子进入中间三角形区域后垂直打在AC边上,求该区域的磁感应强度Bl
(3)若要便带电粒子由FH边界进入FGH区域并能再次回到FH界面,求B2应满足的条件 。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828731701.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828762811.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828778514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828793767.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828809651.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828825751.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028288409360.jpg)
(1)求带电粒子从电场中射出时的速度v的大小和方向
(2)若带电粒子进入中间三角形区域后垂直打在AC边上,求该区域的磁感应强度Bl
(3)若要便带电粒子由FH边界进入FGH区域并能再次回到FH界面,求B2应满足的条件 。
(1)
m/s,与水平方向成30°角斜向下(2)
T(3)
T
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828871704.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828887515.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828918745.png)
试题分析:(1)设带电粒子在电场中做类平抛运动的时间为t,加速度为a,
则:q
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828934461.png)
解得:a=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828949836.png)
t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828965425.png)
竖直方向的速度为
vy=at=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828981419.png)
射出时速度为:v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002828996903.png)
速度v与水平方向夹角为θ,tanθ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829074668.png)
(2)带电粒子出电场时竖直方向的偏转的位移y=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829090338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829105464.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829121433.png)
由几何关系知在磁场ABC区域内做圆周运动的半径为R1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829152794.png)
由B1qv=m
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829168471.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829183883.png)
(3)分析知当轨迹与边界GH相切时,对应磁感应强度B2最大,运动轨迹如图所示:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500282921520102.png)
由几何关系得:R2+
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829230667.png)
故半径R2=(2
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829246344.png)
又B2qv=m
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829277481.png)
故B2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829293550.png)
所以B2应满足的条件为大于
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002829293550.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目