题目内容
(18分)如图所示,空间分布着有理想边界的匀强电场和匀强磁场。左侧匀强电场的场强大小为E、方向水平向右,电场宽度为L;中间区域匀强磁场的磁感应强度大小为B,方向垂直纸面向外。一个质量为m、电量为q、不计重力的带正电的粒子从电场的左边缘的O点由静止开始运动,穿过中间磁场区域进入右侧磁场区域后,又回到O点,然后重复上述运动过程.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035421315630.jpg)
(1)中间磁场区域的宽度d;
(2)带电粒子从O点开始运动到第一次回到O点所用时间t。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035421315630.jpg)
(1)中间磁场区域的宽度d;
(2)带电粒子从O点开始运动到第一次回到O点所用时间t。
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035421781150.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035421621420.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035421781150.png)
试题分析:解析:(1)带电粒子在电场中加速,由动能定理,可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003542193814.png)
带电粒子在磁场中偏转,由牛顿第二定律,可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003542209782.png)
由以上两式,可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003542225990.png)
可见在两磁场区粒子运动半径相同,如图所示,三段圆弧的圆心组成的三角形△O1O2O3是等边三角形,其边长为2R。所以中间磁场区域的宽度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035421621420.png)
2
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035422565836.jpg)
(2)在电场中运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035422711106.png)
在中间磁场中运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003542287959.png)
在右侧磁场中运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035423031026.png)
则粒子第一次回到O点的所用时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250035423181418.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目