题目内容
(18分)扭摆器是同步辐射装置中的插入件,能使粒子的运动轨迹发生扭摆,其简化模型如图所示:Ⅰ、Ⅱ两处宽度均为L的条形匀强磁场区边界竖直,Ⅰ区域磁场垂直纸面向外,Ⅱ区域磁场垂直纸面向里,磁感应强度大小均为B,两磁场区的间距可以调节。以Ⅰ区域左边界上的O点为坐标原点建立坐标系,y轴与左边界重合,x轴与磁场边界的交点分别为O1、O2和O3。一质量为m、电荷量为q的带正电的粒子,平行纸面从O点与y轴的夹角θ=30°射入Ⅰ区域,粒子重力不计。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022415213871.png)
(1)若粒子恰好从O1射出Ⅰ区域,粒子的速度应为多大?
(2)若粒子从Ⅰ区域右边界射出时速度与x轴的夹角为30°,调节两磁场区的间距,粒子恰好从O3射出Ⅱ区域,则粒子从O射入到从O3射出共经历了多长时间?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022415213871.png)
(1)若粒子恰好从O1射出Ⅰ区域,粒子的速度应为多大?
(2)若粒子从Ⅰ区域右边界射出时速度与x轴的夹角为30°,调节两磁场区的间距,粒子恰好从O3射出Ⅱ区域,则粒子从O射入到从O3射出共经历了多长时间?
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241568999.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241537861.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241568999.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022415683840.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022415998281.png)
试题分析:(1)粒子从O1射出Ⅰ区域,轨迹如图
由几何关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241693662.png)
粒子在磁场中运动半径公式为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241708737.png)
综合上式可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241537861.png)
(2)粒子运动轨迹如图所示
设粒子运动速度为v2,半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241740766.png)
粒子在磁场中的运动周期为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241755767.png)
由几何关系可得,粒子在Ⅰ区域运动的圆心角为90°
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241802500.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241818891.png)
由于粒子在Ⅰ、Ⅱ区域运动半径相同,要使粒子从O3射出Ⅱ区域,则粒子在Ⅱ区域中运动时间与Ⅰ
区域相同,且粒子必须经过O1、O2的中点B,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002241833523.png)
在Ⅰ、Ⅱ间隔区域运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022418491503.png)
综上所述,粒子从相同O射入到O3射出共经历时间为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022418641310.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目