题目内容
(14分)如图所示,一个质量为m =2.0×10-11kg,电荷量为q=1.0×10-5C的带正电粒子P(重力忽略不计),从静止开始经U1=100V电压加速后,水平进入两平行金属板间的偏转电场,偏转电场的电压为U2。金属板长L=20cm,两板间距d =20cm,上极板带正电,下极板带负电。粒子经过偏转电场后进入右侧垂直纸面向里的水平匀强磁场中,位于磁场左侧的理想边界紧邻偏转电场,磁场中其余区域没有边界。磁场磁感应强度为B。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500281207017596.jpg)
(1)微粒进入偏转电场时的速度大小?
(2)若粒子一定会由偏转电场进入磁场中,偏转电压U2满足什么条件?
(3)在(2)前提下若粒子离开磁场后不会第二次进入偏转电场,则磁感应强度B应满足什么条件?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500281207017596.jpg)
(1)微粒进入偏转电场时的速度大小?
(2)若粒子一定会由偏转电场进入磁场中,偏转电压U2满足什么条件?
(3)在(2)前提下若粒子离开磁场后不会第二次进入偏转电场,则磁感应强度B应满足什么条件?
(1)
;(2)
;(3)
;
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812086734.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812101661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812117515.png)
试题分析:(1)微粒在加速电场中由动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812133839.png)
代入数据解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812086734.png)
(2)粒子在偏转电场中有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812179465.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812195774.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812211645.png)
故解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028122261037.png)
若粒子一定能进入磁场中,则满足:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812242592.png)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028122731211.png)
(3)当粒子以速度v与水平成
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812289297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028123358119.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812351763.png)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812367668.png)
进入磁场与离开磁场的位置间的距离为x,则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028123981099.png)
粒子在偏转电场中做类平抛运动有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812413572.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812429783.png)
若粒子不再第二次进入偏转电场,则当
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812460563.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812476436.png)
即 :
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812491842.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002812507998.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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