题目内容
如图所示:在真空中,半径为
的圆形区域内存在匀强磁场,磁场方向垂直纸面向里,在磁场右侧有一对平行金属板
和
,两板间距离为
,板长为
,板的中心线
与磁场的圆心
在同一直线上,有一电荷量为
、质量为
的带电的粒子,以速度
从圆周上的
点沿垂直于半径
并指向圆心的方向进入磁场平面,当从圆周上的
点水平飞出磁场时,给
、
板加上如下图所示电压,最后粒子刚好以平行于
板的速度,从
板的边缘飞出(不计粒子重力),求
(1)磁场的磁感应强度;
(2)求交变电压的周期
和电压
的值;
(3)若
时,该粒子从
、
板右侧沿板的中心线仍以速率
向左射入
、
之间,求粒子从磁场中射出的点到
点的距离?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136065416311.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605449486.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605496384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605542502.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605558474.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605652398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605683293.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605698297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605714333.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605745305.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605761277.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605792361.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605823323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605496384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605496384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605496384.png)
(1)磁场的磁感应强度;
(2)求交变电压的周期
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605948273.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605979343.png)
(3)若
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606010541.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605496384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605745305.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605496384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605761277.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136065416311.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606634790.png)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606650900.png)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606697687.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606634790.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606650900.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606697687.png)
(1)粒子由
点进入磁场在洛仑兹力作用下做圆周运动,所以![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606822815.png)
由题意知粒子圆周运动的半径:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606837570.png)
解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606634790.png)
(2)据题意,粒子在电场中的运动时间为电场变化周期的整数倍,即:
,于是得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606978748.png)
粒子在电场中运动侧向总位移:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136070401348.png)
带入已知量解得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606650900.png)
(3)由粒子在磁场中的受力可判断粒子带负电,粒子在
时刻进入电场后向
板偏转,由题意知粒子应刚好平行于
板从
板的边缘水平飞出,并沿着水平方向进入磁场。
如图:设粒子从
点进入磁场,从
点射出,
点为粒子圆周运动的圆心,可知:
,所以
为菱形,故有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607321549.png)
由于粒子水平射出,故
,于是
,方向竖直,故
点共线,所以射出的点到
点的距为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606697687.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136074926298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605761277.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606822815.png)
由题意知粒子圆周运动的半径:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606837570.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136068845127.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606634790.png)
(2)据题意,粒子在电场中的运动时间为电场变化周期的整数倍,即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606946679.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606978748.png)
粒子在电场中运动侧向总位移:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136070401348.png)
带入已知量解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606650900.png)
(3)由粒子在磁场中的受力可判断粒子带负电,粒子在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607087544.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605527342.png)
如图:设粒子从
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607180305.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607212299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607227339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607258407.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607305519.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607321549.png)
由于粒子水平射出,故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607336534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607368499.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113607383435.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113605761277.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113606697687.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241136074926298.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目