题目内容
从阴极K发射的电子经电势差U0=5000V的阳极加速后,沿平行于板面的方向从中央射入两块长L1=10cm、间距d=4cm的平行金属板A、B之间,在离金属板边缘L2=75cm处放置一个直径D=20cm、带有纪录纸的圆筒。整个装置放在真空内,电子发射时的初速度不计,如图6所示,若在金属板上加一U=1000cos2πt V的交流电压,并使圆筒绕中心轴按图示方向以n=2r/s匀速转动,分析电子在纪录纸上的轨迹形状并画出从t=0开始的1s内所纪录到的图形
。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215595542009.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215596161733.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215596471391.gif)
对电子的加速过程,由动能定理得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215597881384.gif)
eU0=
mv02![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
得电子加速后的速度 v0=
=4.2×107m/s![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子进入偏转电场后,由于在其中运动的时间极短,可以忽略运动期间偏转电压的变化,认为电场是稳定的,因此电子做类平抛的运动。如图7所示。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
交流电压在A、B两板间产生的电场强度
V/m![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子飞离金属板时的偏转距离![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600115831.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子飞离金属板时的竖直速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600162671.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子从飞离金属板到到达圆筒时的偏转距离![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600505727.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
所以在纸筒上的落点对入射方向的总偏转距离为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
m![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
可见,在纪录纸上的点在竖直方向上以振幅0.20m、周期T=1s做简谐运动。因为圆筒每秒转2周,故转一周在纸上留下的是前半个余弦图形,接着的一周中,留下后半个图形,合起来,1s内,在纸上的图形如图8所示。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215597881384.gif)
eU0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559803225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
得电子加速后的速度 v0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559835526.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241215599131444.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
交流电压在A、B两板间产生的电场强度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600100737.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子飞离金属板时的偏转距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600115831.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子飞离金属板时的竖直速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600162671.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
电子从飞离金属板到到达圆筒时的偏转距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121600505727.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
所以在纸筒上的落点对入射方向的总偏转距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241216005521736.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
可见,在纪录纸上的点在竖直方向上以振幅0.20m、周期T=1s做简谐运动。因为圆筒每秒转2周,故转一周在纸上留下的是前半个余弦图形,接着的一周中,留下后半个图形,合起来,1s内,在纸上的图形如图8所示。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121559569333.jpg)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目