题目内容
(16分)如图所示,平行板电容器上板M带正电,两板间电压恒为U,极板长为(1+
)d,板间距离为2d,在两板间有一圆形匀强磁场区域,磁场边界与两板及右侧边缘线相切,P点是磁场边界与下板N的切点,磁场方向垂直于纸面向里,现有一带电微粒从板的左侧进入磁场,若微粒从两板的正中间以大小为v0水平速度进入板间电场,恰做匀速直线运动,经圆形磁场偏转后打在P点。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250042039268620.png)
(1)判断微粒的带电性质并求其电荷量与质量的比值;
(2)求匀强磁场的磁感应强度B的大小;
(3)若带电微粒从M板左侧边缘沿正对磁场圆心的方向射入板间电场,要使微粒不与两板相碰并从极板左侧射出,求微粒入射速度的大小范围。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203895344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250042039268620.png)
(1)判断微粒的带电性质并求其电荷量与质量的比值;
(2)求匀强磁场的磁感应强度B的大小;
(3)若带电微粒从M板左侧边缘沿正对磁场圆心的方向射入板间电场,要使微粒不与两板相碰并从极板左侧射出,求微粒入射速度的大小范围。
负电
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203973624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250042039883938.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203942831.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203957787.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203973624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250042039883938.png)
试题分析:(1)由题意可知,微粒所受电场力向上,上板带正电可得微粒带负电,(1分)
由于微粒做匀速直线运动可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204004588.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204020655.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203942831.png)
(2) 由题意可得,微粒从下板P垂直射出,所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204066442.png)
根据牛顿第二定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204082754.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250042040981051.png)
(3)如图所示,要使粒子从左板射出,临界条件是恰从下板左边射出,此时根据几何关系可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204113777.png)
微粒做圆周运动的半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204129882.png)
又根据牛顿第二定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204144796.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004204160599.png)
要使微粒从左板射出
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004203973624.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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