2016年泛珠三角物理竞赛综合试卷一题.pdf

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) Please fill in your final answers to all problems on the summary sheet. 请在总答案纸上填上各题的最后答案。 There are 5 problems. Please answer each problem using a new sheet. 卷一5 题，每答1 题，须采用新一张纸。 Please answer on each sheet using a single column. Do not use two columns on a single sheet. 每页纸请用单一直列的方式答题。不可以在一页纸上以双直列方式答题。 Please answer on only one side of each sheet. Do not use both sides of the sheet. 每张纸单面作答。不可以双面作答。 At the end of the competition, please arrange the summary sheet as the first page, followed by the answers to each problem in sequential order of the problems. If your answer to a problem requires more than one sheet, please arrange the sheets of the same problem in sequential order of the parts. 比赛结束时，请将总答案纸放在首页，随后把答题纸按题目次序排好。若答一题超过一 页，请按分部次序排好答题纸。 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。 2. Capacitors (13 marks) (a-c) Consider two clusters of electric charges. Cluster A consists of N charges q , q , …, q , 1 2 N