题目内容
(20分)如图所示为一空间直角坐标系xoy,在
和MN之间的区域内,有宽度为d、沿y轴正方向的匀强电场,电场强度为E。有一质量为m、电量为
的电子,由静止开始经过另一电势差为U的电场加速后,从
轴上的P点(坐标0、
),沿x轴正方向射入电场(电子重力不计)。
(1)求电子能够从x轴上方飞离电场区域,加速电场的电势差U应满足什么条件?
(2)若电子从右边界MN上某点射出后,运动到x轴上的Q点,求Q点的横坐标。(加速电压U已知)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241223080713087.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308009221.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308024185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308040193.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308055200.gif)
(1)求电子能够从x轴上方飞离电场区域,加速电场的电势差U应满足什么条件?
(2)若电子从右边界MN上某点射出后,运动到x轴上的Q点,求Q点的横坐标。(加速电压U已知)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241223080713087.jpg)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308087507.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308149586.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308087507.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308149586.gif)
(1)电子经加速后,到达P点的速度为
,由动能定理
…………(3分)
电子在电场中做类平抛运动,则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241223081963214.jpg)
…………(1分)
…………(1分)
…………(1分)
解得
…………(2分)
若电子能够从
轴上方飞离电场区域,则
…………………(1分)
综上解得:
即为所求……………………(2分)
(2)电子从MN上某点射出时,速度v的方向与水平方向成
角。
…………(3分)
设NQ的长度为
,
…………(2分)
则的横坐标
…………(1分)
解得
…………(3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308165204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308180537.gif)
电子在电场中做类平抛运动,则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241223081963214.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308196384.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308227445.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308321444.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308336504.gif)
若电子能够从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308352187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308383358.gif)
综上解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308087507.gif)
(2)电子从MN上某点射出时,速度v的方向与水平方向成
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308414192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308430598.gif)
设NQ的长度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308430185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308445510.gif)
则的横坐标
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308461369.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122308149586.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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