题目内容
在竖直平面内建立一平面直角坐标系xoy,x轴沿水平方向,如图甲所示。第二象限内有一水平向右的匀强电场,场强为E1。坐标系的第一、四象限内有一正交的匀强电场和匀强交变磁场,电场方向竖直向上,场强
,匀强磁场方向垂直纸面。处在第三象限的某种发射装置(图中没有画出)竖直向上射出一个比荷
的带正电的微粒(可视为质点),该微粒以v0=4m/s的速度从-x上的A点进入第二象限,并以v1=8m/s速度从+y上的C点沿水平方向进入第一象限。取微粒刚进入第一象限的时刻为0时刻,磁感应强度按图乙所示规律变化(以垂直纸面向外的磁场方向为正方向),g="10" m/s2.试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241350592896809.png)
⑴带电微粒运动到C点的纵坐标值h及电场强度E1 ;
⑵+x轴上有一点D,OD=OC,若带电微粒在通过C点后的运动过程中不再越过y轴,要使其恰能沿x轴正方向通过D点,求磁感应强度B0及其磁场的变化周期T0为多少?
⑶要使带电微粒通过C点后的运动过程中不再越过y轴,求交变磁场磁感应强度B0和变化周期T0的乘积B0 T0应满足的关系?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135058587542.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135058696832.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241350592896809.png)
⑴带电微粒运动到C点的纵坐标值h及电场强度E1 ;
⑵+x轴上有一点D,OD=OC,若带电微粒在通过C点后的运动过程中不再越过y轴,要使其恰能沿x轴正方向通过D点,求磁感应强度B0及其磁场的变化周期T0为多少?
⑶要使带电微粒通过C点后的运动过程中不再越过y轴,求交变磁场磁感应强度B0和变化周期T0的乘积B0 T0应满足的关系?
⑴
, (2分)
(2分)
,
,
(3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351001781553.png)
⑵
,所以带电的粒子在第一象限将做匀速圆周运动,设粒子运动圆轨道半径为R,周期为T,则
可得
(2分)
使粒子从C点运动到D点,则有:
(2分)
(1分)
(2分)
,
(2分)
⑶当交变磁场周期取最大值而粒子不再越过y轴时可作如图运动情形:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351010361794.png)
由图可知
(2分)
(2分)
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135059336715.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135059523891.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135059585723.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135059960674.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100038724.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351001781553.png)
⑵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100209632.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100256877.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100303658.png)
使粒子从C点运动到D点,则有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351003651135.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100568991.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100599817.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135100958580.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351009891579.png)
⑶当交变磁场周期取最大值而粒子不再越过y轴时可作如图运动情形:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351010361794.png)
由图可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135101067612.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351011141021.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241351011451067.png)
本题考查的是电场磁场的结合问题,学生要熟悉带电粒子在电场和磁场的运动规律。
![](http://thumb2018.1010pic.com/images/loading.gif)
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