题目内容
(1)粒子刚穿出第一个有电场和磁场分布的区域时,其速度的水平分量vx为多大?
(2)如图2所示,粒子穿过其中任意一个有电场和磁场分布的区域时,其速度的水平分量的变化量△vx为多大?
(3)求粒子到达第几个有电场和磁场分布的区域时,带电粒子不能从该区域的下方射出来?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082411542979023454.jpg)
(1) 0.18m (2) 0.18m(3)粒子不能穿过第61个有电场和磁场的区域
(1)(6分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154298537143.jpg)
如上图,设粒子刚进入第一个有电场和磁场分布的区域时速度为v,由于qE=mg,所以粒子在里面作匀速圆周运动,设出第一个区域时与水平方向夹角为θ,则:
vx=vcosθ 又
即
代入得 vx=
=
=0.18m
(2)(7分)设粒子进入任意一个有电场和磁场分布的区域时速度为v,粒子作匀速圆周运动,设进入区域时与水平方向夹角为α,出区域时与水平方向夹角为β,则:
; 又![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115429884473.gif)
得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082411543030573.gif)
=
=0.18m
(3)(7分)设刚好能从第n个有磁场和电场的区域内射出(或不射出)
由能量关系有
在最低点,速度水平,即
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430477734.gif)
故粒子不能穿过第61个有电场和磁场的区域
注意:此题也可以用微元的思想
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154298537143.jpg)
如上图,设粒子刚进入第一个有电场和磁场分布的区域时速度为v,由于qE=mg,所以粒子在里面作匀速圆周运动,设出第一个区域时与水平方向夹角为θ,则:
vx=vcosθ 又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115429853520.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115429884473.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430102700.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430149397.gif)
(2)(7分)设粒子进入任意一个有电场和磁场分布的区域时速度为v,粒子作匀速圆周运动,设进入区域时与水平方向夹角为α,出区域时与水平方向夹角为β,则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430227610.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115429884473.gif)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082411543030573.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154303361703.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430149397.gif)
(3)(7分)设刚好能从第n个有磁场和电场的区域内射出(或不射出)
由能量关系有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430383593.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430399486.gif)
在最低点,速度水平,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430414688.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430461639.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115430477734.gif)
故粒子不能穿过第61个有电场和磁场的区域
注意:此题也可以用微元的思想
![](http://thumb2018.1010pic.com/images/loading.gif)
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