题目内容
如图所示,空间存在垂直XOY平面向里的匀强磁场,MN为一荧光屏,上下两面均可发光,当带电粒子打到屏上某点时,即可使该点发光,荧光屏位置如图,坐标为M(0,4.0),N(4.0,4.0)单位为cm。坐标原点O有一粒子源,可以发射沿XOY平面各个方向的电子(不计电子的重力),已知电子质量m=9.0×10-31kg,电量为e=1.6×10-19C,磁感应强度B=9.0×10-3T,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241239549127513.jpg)
(1)若一电子以
沿y轴正方向射入,求荧光屏上亮点坐标。
(2)若所有电子以
射入,求能打到M点的电子的速度入射方向。(用与X轴正方向的夹角或夹角的三角函数值表示)
(3)若所有电子以
射入,求荧光屏发光区域的坐标(坐标的单位为 cm)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241239549127513.jpg)
(1)若一电子以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123954928567.gif)
(2)若所有电子以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123954943565.gif)
(3)若所有电子以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123954943565.gif)
略
(1)
…① ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123954990554.gif)
由几何关系可知:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
…②
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
坐标为(2,4)cm…③
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
,
,…④能打到M点的
粒子轨迹如图1圆a和圆b所示
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241239553653699.gif)
由几何关系:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955380491.gif)
…⑤, ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955443286.gif)
所以
…⑥,
…⑦
(3)
,
若打在下方最远点,如图2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241239555212996.gif)
所示为相切,由几何关系可知:
…⑧所以
,坐标为(0,4)到(2,4)cm…⑨
若打在上方最远点,如图则轨迹圆左端刚好打在M点则:
…⑩
所以
坐标为(0,4)到(3,4)cm…⑾
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123954975468.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123954990554.gif)
由几何关系可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955021543.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955115422.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955131528.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955146438.gif)
粒子轨迹如图1圆a和圆b所示
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241239553653699.gif)
由几何关系:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955380491.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412395500673.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955443286.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955458622.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955474619.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955131528.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955146438.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241239555212996.gif)
所示为相切,由几何关系可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955536592.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955115422.gif)
若打在上方最远点,如图则轨迹圆左端刚好打在M点则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955567493.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123955583436.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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