题目内容
(16分)如图所示,在xoy平面直角坐标系的第一象限有射线OA,OA与x轴正方向夹角为30°,OA与y轴所夹区域内有沿y轴负方向的匀强电场,其他区域存在垂直于坐标平面向外的匀强磁场。有一质量为m、电量为q的带正电粒子,从y轴上的P点沿着x轴正方向以初速度v0射入电场,运动一段时间后经过Q点垂直于射线OA进入磁场,经磁场偏转,过y轴正半轴上的M点再次垂直进入匀强电场。已知OP=h,不计粒子重力,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082414325368614570.png)
(1)粒子经过Q点时的速度大小;
(2)匀强电场电场强度的大小;
(3)粒子从Q点运动到M点所用的时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082414325368614570.png)
(1)粒子经过Q点时的速度大小;
(2)匀强电场电场强度的大小;
(3)粒子从Q点运动到M点所用的时间。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254138771.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143253857803.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254076912.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254138771.png)
⑴粒子类平抛到Q点时将速度分解如图。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143253857803.png)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254279916.png)
P到Q类平抛,得
X方向:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254341828.png)
Y方向:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241432544351085.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254669676.png)
竖直方向![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254715753.png)
解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254076912.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082414325493411509.png)
⑶由题得,磁偏转的半径
,
由
及
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255745883.png)
Q到M点,圆心角![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255885579.png)
则运动时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255948800.png)
代入磁感应强度B,得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254138771.png)
本题考查带电粒子在复合场中的运动,难度较大,粒子在电场中做类平抛运动,把末速度分解,可求得Q点的合速度,根据平抛运动特点,把位移分解,列公式求解电场强度E的大小,由几何关系可知粒子在磁场中的偏转半径,由洛伦兹力提供向心力可求得磁感强度和周期大小,求得弧线对应圆心角大小,再求运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143253857803.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254279916.png)
P到Q类平抛,得
X方向:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254341828.png)
Y方向:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241432544351085.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254591776.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254669676.png)
竖直方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254715753.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254076912.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082414325493411509.png)
⑶由题得,磁偏转的半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255324723.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255480755.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255558667.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255605791.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255745883.png)
Q到M点,圆心角
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255885579.png)
则运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143255948800.png)
代入磁感应强度B,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824143254138771.png)
本题考查带电粒子在复合场中的运动,难度较大,粒子在电场中做类平抛运动,把末速度分解,可求得Q点的合速度,根据平抛运动特点,把位移分解,列公式求解电场强度E的大小,由几何关系可知粒子在磁场中的偏转半径,由洛伦兹力提供向心力可求得磁感强度和周期大小,求得弧线对应圆心角大小,再求运动时间
![](http://thumb2018.1010pic.com/images/loading.gif)
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