题目内容
如图所示,一质量为m电荷量q的带电微粒,从静止开始经电压为U1的电场加速后,水平进入两平行金属板间的偏转电场中,微粒射出电场时的偏转角为θ。已知偏转电场中金属板长度为L,两板间距为d,重力忽略不计。求:
小题1:带电微粒进入偏转电场时的速率v1
小题2:偏转电场中两金属板间的电压U2![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319176774518.png)
小题1:带电微粒进入偏转电场时的速率v1
小题2:偏转电场中两金属板间的电压U2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319176774518.png)
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131917724320.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131917739430.png)
(1)粒子在加速电场中,电场力做功,由动能定理求出速度v0.
(2)粒子进入偏转电场后,做类平抛运动,运用运动的合成与分解求出电压.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319177866526.png)
解:(1)带电微粒经加速电场加速后速度为v,根据动能定理U1q=
mv12
v1=
(2)带电微粒在偏转电场中只受电场力作用,做类平抛运动.在水平方向微粒做匀速直线运动
水平方向:v1=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131917911290.png)
带电微粒在竖直方向做匀加速直线运动,加速度为a,出电场时竖直方向速度为v2
竖直方向:a=
=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918129522.png)
v2=at=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918129522.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918192182.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918223370.png)
由几何关系 tanθ=
=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918316905.png)
U2=
tanθ
(2)粒子进入偏转电场后,做类平抛运动,运用运动的合成与分解求出电压.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241319177866526.png)
解:(1)带电微粒经加速电场加速后速度为v,根据动能定理U1q=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131917817338.png)
v1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131917864736.png)
(2)带电微粒在偏转电场中只受电场力作用,做类平抛运动.在水平方向微粒做匀速直线运动
水平方向:v1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131917911290.png)
带电微粒在竖直方向做匀加速直线运动,加速度为a,出电场时竖直方向速度为v2
竖直方向:a=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918098417.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918129522.png)
v2=at=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918129522.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918192182.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918223370.png)
由几何关系 tanθ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918270418.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918316905.png)
U2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824131918363505.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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