题目内容
(20分)如图所示,一质量为m、电荷量为q、重力不计的微粒,从倾斜放置的平行电容器I的A板处由静止释放,A、B间电压为U1。微粒经加速后,从D板左边缘进入一水平放置的平行板电容器II,由C板右边缘且平行于极板方向射出,已知电容器II的板长为板间距离的2倍。电容器右侧竖直面MN与PQ之间的足够大空间中存在着水平向右的匀强磁场(图中未画出),MN与PQ之间的距离为L,磁感应强度大小为B,在微粒的运动路径上有一厚度不计的窄塑料板(垂直纸面方向的宽度很小),斜放在MN与PQ之间,
=45°。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011344644769.jpg)
(1)微粒从电容器I加速后的速度大小;
(2)电容器IICD间的电压;
(3)假设粒子与塑料板碰撞后,电量和速度大小不变、方向变化遵循光的反射定律,碰撞时间极短忽略不计,微粒在MN与PQ之间运动的时间和路程。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134448310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011344644769.jpg)
(1)微粒从电容器I加速后的速度大小;
(2)电容器IICD间的电压;
(3)假设粒子与塑料板碰撞后,电量和速度大小不变、方向变化遵循光的反射定律,碰撞时间极短忽略不计,微粒在MN与PQ之间运动的时间和路程。
(1)
(2)
(3)
;![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011345421003.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134480730.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134511499.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011345261121.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011345421003.png)
试题分析:(1)在电容器I中,由动能定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134558889.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134573840.png)
(2)粒子进入电容器II做类斜抛运动。设微粒进入电容器II时的速度方向与水平方向的夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134589292.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134604734.png)
垂直板方向:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011346671270.png)
离开板间时垂直板方向速度减为零即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011346821087.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134714492.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134729614.png)
(3)微粒进入磁场后速度平行于磁场方向,做匀速直线运动;第一次碰板后速度垂直于磁场方向做匀速圆周运动;二次碰板后做匀速直线运动。
微粒进入磁场的速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011347451077.png)
微粒做匀速圆周运动:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134901812.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134932702.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134948735.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001134963767.png)
微粒在MN和PQ间的运动路程
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011349941262.png)
运动时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011350101375.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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