题目内容
(20分)静电喷漆技术具有效率高、浪费少、质量好、有益于健康等优点,其装置可简化如图。
、
为水平放置的间距
的两块足够大的平行金属板,两板间有方向由
指向
的匀强电场,场强为
。在
板的中央放置一个安全接地的静电油漆喷枪
,油漆喷枪可向各个方向均匀地喷出初速度大小均为
的油漆微粒,已知油漆微粒的质量均为
、电荷量均为
,不计油漆微粒间的相互作用、油漆微粒带电对板间电场和磁场的影响及空气阻力,重力加速度
。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050315351521.png)
(1)油漆微粒落在
板上所形成的图形面积;
(2)若让
、
两板间的电场反向,并在两板间加垂直于纸面向里的匀强磁场,磁感应强度
,调节喷枪使油漆微粒只能在纸面内沿各个方向喷出,其它条件不变。
板被油漆微粒打中的区域的长度;
(3) 在满足(2)的情况下,打中
板的油漆微粒中,在磁场中运动的最短时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031270300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031317525.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031270300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031364591.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031270300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031395289.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031426589.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031457726.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031473674.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031488618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050315041401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050315351521.png)
(1)油漆微粒落在
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
(2)若让
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031270300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031613518.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
(3) 在满足(2)的情况下,打中
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
(1)18.1m2 (2)1.6m (3)0.31s
试题分析:(1)油漆微粒的加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031676794.png)
根据运动学规律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031691668.png)
运动的半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031722492.png)
落在
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031754495.png)
由①②③式并代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031769560.png)
(2)当电场反向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031785593.png)
油漆微粒做匀速圆周运动,洛伦兹力充当向心力
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031910782.png)
水平向右射出的油漆微粒打在
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031941690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031956325.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031988477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032003169.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050320344364.png)
打在
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032066437.png)
油漆微粒打在极板上的长度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032081542.png)
由⑥⑦⑧⑨⑩11式并代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032112557.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050321283688.png)
(3)打在
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005031286309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032175361.png)
有几何关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032190778.png)
运动的最短时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032206790.png)
微粒在磁场中运动的周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032237771.png)
由7131415式代入数据解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005032253629.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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