2024年3月16日发(作者：)

Pan Pearl River Delta Physics Olympiad 2016

2016 年泛珠三角及中华名校物理奥林匹克邀请赛

Sponsored by Institute for Advanced Study, HKUST

香港科技大学高等研究院赞助

Simplified Chinese Part-1 (Total 5 Problems) 简体版卷-1（共5题）

(9:00 am – 12:00 pm, 18 February, 2016)

1. Electrostatic Force (4 marks) 静电力 （4分）

Consider a 2017-side regular polygon. There are 2016 point charges, each with charge q and

located at a vertex of the polygon. Another point charge Q is located at the center of the

polygon. The distance from the center of the regular polygon to its vertices is a. Find the

force experienced by Q.

考虑一2017-边正多边形。其中2016个角上各有一点电荷q。 另有一个点电荷Q位于

多边形的中心。 中心到每一个角的距离为a。 求Q所受的力。

Consider the polygon with a charge q at each vertex. In other words, there are 2017 charges. The

system has a discrete rotational symmetry and hence the force acting on Q must be zero. Now

our system is equivalent to the above system but with a charge –q added to one vertex. Hence the

force is