题目内容
如图所示,带电量分别为4q和-q的小球A、B固定在水平放置的光滑绝缘细杆上,相距为d.若杆上套一带电小环C,带电体A、B和C均可视为点电荷.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241516021361116.png)
(1)求小环C的平衡位置.
(2)若小环C带电量为q,将小环拉离平衡位置一小位移x(|x|《d)后静止释放,试判断小环C能否回到平衡位置.(回答“能”或“不能”即可)
(3)若小环C带电量为-q,将小环拉离平衡位置一小位移x(|x|《d)后静止释放,试证明小环C将作简谐动.(提示:当α《1时,则
≈1-nα)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241516021361116.png)
(1)求小环C的平衡位置.
(2)若小环C带电量为q,将小环拉离平衡位置一小位移x(|x|《d)后静止释放,试判断小环C能否回到平衡位置.(回答“能”或“不能”即可)
(3)若小环C带电量为-q,将小环拉离平衡位置一小位移x(|x|《d)后静止释放,试证明小环C将作简谐动.(提示:当α《1时,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602230533.png)
(1)在AB连线的延长线上距离B为d处 (2)不能 (3)见解析
(1)设C在AB连线的延长线上距离B为l处达到平衡,带电量为Q库仑定律F=k![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602292510.png)
平衡条件FC=
+
=0
解得
1=-
d(舍去),
2=d?所以,平衡位置
=d
(2)不能?
(3)小环C带电量为-q,平衡位置不变,拉离平衡位置一小位移x后
C受力为FC=
+![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602978798.png)
利用近似关系化简得FC=-
x.
所以小环C将做简谐运动
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602292510.png)
平衡条件FC=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602370862.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602495610.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602573180.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602651327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602573180.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602573180.png)
(2)不能?
(3)小环C带电量为-q,平衡位置不变,拉离平衡位置一小位移x后
C受力为FC=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602885928.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151602978798.png)
利用近似关系化简得FC=-
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151603103630.png)
所以小环C将做简谐运动
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目