题目内容
(16分)如图所示,在坐标系的第一、四象限存在一宽度为a、垂直纸面向外的有界匀强磁场,磁感应强度的大小为B;在第三象限存在与y轴正方向成θ=60°角的匀强电场。一个粒子源能释放质量为m、电荷量为+q的粒子,粒子的初速度可以忽略。粒子源在点P(
,
)时发出的粒子恰好垂直磁场边界EF射出;将粒子源沿直线PO移动到Q点时,所发出的粒子恰好不能从EF射出。不计粒子的重力及粒子间相互作用力。求:
⑴匀强电场的电场强度;
⑵PQ的长度;
⑶若仅将电场方向沿顺时针方向转动60º角,粒子源仍在PQ间移动并释放粒子,试判断这些粒子第一次从哪个边界射出磁场并确定射出点的纵坐标范围。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032101893816.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003209939566.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003209955454.png)
⑴匀强电场的电场强度;
⑵PQ的长度;
⑶若仅将电场方向沿顺时针方向转动60º角,粒子源仍在PQ间移动并释放粒子,试判断这些粒子第一次从哪个边界射出磁场并确定射出点的纵坐标范围。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032101893816.png)
(1)
(2)
(3)[
,
]
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210205827.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210236879.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210251780.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210267650.png)
试题分析:(1)粒子源在P点时,粒子在电场中被加速
根据动能定理 有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210298846.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210314862.png)
粒子在磁场中做匀速圆周运动,根据牛顿第二定律 有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210329834.png)
由几何关系知,半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210345785.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032103765465.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210205827.png)
(2)粒子源在Q点时,设OQ=d
根据动能定理 有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210407872.png)
根据牛顿第二定律 有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210439850.png)
粒子在磁场中运动轨迹与边界EF相切,由几何关系知
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210454784.png)
联立解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210470532.png)
长度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210236879.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032105175485.png)
(3)若仅将电场方向沿顺时针方向转动
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210532399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210548501.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210563637.png)
从P发出的粒子第一次从y轴上N点射出,由几何关系知轨道正好与EF相切,N点的纵坐标
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032105791350.png)
同理可求,从Q发出的粒子第一次从y轴上M点射出,M点的纵坐标
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032105951666.png)
即射出点的纵坐标范围 [
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210251780.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003210267650.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032106577050.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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