题目内容
(18分)如图,带电量为+q、质量为m的粒子(不计重力)由静止开始经A、B间电场加速后,沿中心线匀速射入带电金属板C、D间,后粒子由小孔M沿径向射入一半径为R的绝缘筒,已知C、D间电压为U0,板间距离为d,C、D间与绝缘筒内均有垂直于纸面向里的匀强磁场,磁感应强度分别为B0、B.
(1)(6分)求粒子在C、D间穿过时的速度v0;
(2)(6分)求A、B间的加速电压U;
(3)(6分)粒子与绝缘筒壁碰撞,速率、电荷量都不变,为使粒子在筒内能与筒壁碰撞4次(不含从M孔出来的一次)后又从M孔飞出,求筒内磁感应强度B (用三角函数表示).
(1)(6分)求粒子在C、D间穿过时的速度v0;
(2)(6分)求A、B间的加速电压U;
(3)(6分)粒子与绝缘筒壁碰撞,速率、电荷量都不变,为使粒子在筒内能与筒壁碰撞4次(不含从M孔出来的一次)后又从M孔飞出,求筒内磁感应强度B (用三角函数表示).
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222406306490.jpg)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240662380.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240662655.gif)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240693878.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240662380.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240662655.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240693878.gif)
(1)∵粒子在C、D间做匀速运动,则:
Eq=B0qv0……...2分 而
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240708323.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240662380.gif)
(2)粒子在A、B间加速过程有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240724545.gif)
且E=U0/d ……...1分 解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240662655.gif)
(3)带电离子在圆形磁场中运动的可能轨迹如图:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222407716612.jpg)
由(1)得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240786491.gif)
离子在圆形磁场中有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240802555.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240818744.gif)
如图所示:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240833532.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240849200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240864196.gif)
第一种情况:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240896421.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240911501.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222409271101.gif)
第二种情况:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240849200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240958262.gif)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122240974546.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222409891127.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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