题目内容
(18分)如图甲所示,在坐标系
中,
轴左侧有沿
轴正向的匀强电场,场强大小为E;
轴右侧有如图乙所示,大小和方向周期性变化的匀强磁场,磁感强度大小B0已知.磁场方向垂直纸面向里为正.
时刻,从
轴上的p点无初速释放一带正电的粒子,质量为m,电量为q(粒子重力不计),粒子第一次在电场中运动时间与第一次在磁场中运动的时间相等.求
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012206096348.jpg)
(1)P点到O点的距离;
(2)粒子经一个周期沿y轴发生的位移;
(3)粒子能否再次经过O点,若不能说明理由.若能,求粒子再次经过O点的时刻;
(4)粒子第4n(n=1、2、3 )次经过y轴时的纵坐标.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220250413.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220266310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220281266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220266310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220546363.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220281266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012206096348.jpg)
(1)P点到O点的距离;
(2)粒子经一个周期沿y轴发生的位移;
(3)粒子能否再次经过O点,若不能说明理由.若能,求粒子再次经过O点的时刻;
(4)粒子第4n(n=1、2、3 )次经过y轴时的纵坐标.
试题分析:(1)粒子在电场中匀加速运动时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220624319.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220640752.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220671585.png)
OP间距离为x,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220687628.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220702937.png)
(2)粒子圆周运动的半径分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220718327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220734361.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220749780.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220780890.png)
粒子每经一个周期沿y轴向下移动
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220796383.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012208121193.png)
(3)当粒子从左侧射入向上偏转时可能再次经过O点,故从O点下方
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220827409.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220890671.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220905463.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220936569.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220983864.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001221030811.png)
(4)经过分析知粒子每个周期4次经过y轴,每个周期沿y轴移动距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001220796383.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001221061699.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001221092952.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目