题目内容
(17分)如图所示的平面直角坐标系xOy,在第Ⅰ象限内有平行于y轴的匀强电场,方向沿y正方向;在第Ⅳ象限的正方形abcd区域内有匀强磁场,方向垂直于xOy平面向里,正方形边长为L且ad边与x轴重合,ab边与y轴平行.一质量为m、电荷量为q的粒子,从y轴上的P(0,h)点,以大小为v0的速度沿x轴正方向射入电场,通过电场后从x轴上的a(2h,0)点进入第Ⅳ象限的磁场区域,不计粒子所受的重力.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035034746898.jpg)
(1)电场强度E的大小;
(2)粒子到达a点时速度的大小和方向;
(3)磁感应强度B满足什么条件,粒子经过磁场后能到达y轴上,且速度与y轴负方向成450角?
(4)磁感应强度B满足什么条件,粒子经过磁场后不能到达y轴上?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035034746898.jpg)
(1)电场强度E的大小;
(2)粒子到达a点时速度的大小和方向;
(3)磁感应强度B满足什么条件,粒子经过磁场后能到达y轴上,且速度与y轴负方向成450角?
(4)磁感应强度B满足什么条件,粒子经过磁场后不能到达y轴上?
(1)
(2)
,放行与x轴正方向成45度角 (3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503536810.png)
(4)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503552746.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503505848.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503521556.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503536810.png)
(4)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503552746.png)
试题分析:(1)粒子做类平抛运动
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503568851.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503505848.png)
(2)到达a点时水平速度为v0,竖直速度vy
水平方向2h=v0t 竖直方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503599662.png)
得:vy=v0
所以到达a点的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503521556.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035036469609.jpg)
(3)粒子到达y轴上,且速度与y轴负方向成45度角,必须要从ab边射出,从b点射出对应的此时磁感应强度B1最小,粒子在磁场中的轨迹以O1为圆心一段四分之一圆弧,设半径为r1,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503661623.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503677867.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503708822.png)
所以磁感应强度须满足的条件:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503536810.png)
(4)粒子恰好不能到达y轴上,此时粒子垂直bc边射出,对应的此时磁感应强度B2,粒子在磁场中的轨迹以O2为圆心一段八分之一圆弧,
设半径为r2,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503739551.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503755885.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503786761.png)
所以磁感应强度须满足的条件
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003503552746.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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