2021-P1 Best Solutions and Final Results

Problem 1 – Dumbbell in a magnetic field

By 18th February 2021, there are 976 registered participants from 71 countries. In total, 97 solutions were submitted for problem 1, out of which 31 were correct.

As usual, when selecting the best solutions, preference has been given to those solutions which have been submitted before the publication of the first hint. Overall, there were eight such solutions: from Vlad-Ștefan Oros, Oliwier Urbański, Zhening Li, Elio Moreau, Eddie Chen, Antonia Ghita, Joshua Teo, Nikita Semenin.

With this problem, it was easy to overlook the fact that in the initial value of the generalized momentum, the dominating contribution is given by the polarization of the balls. Missing this fact did not mean as much lacking in physics, but being slightly careless, and the formula would have been accurate enough if the magnetic field had been a few times weaker (similarly I have been overlooking all geometry-related mistakes by a small parameter R/L). Keeping in mind this, together with the fact that it was a really difficult problem, all submissions with this mistake had been considered as correct ones.

However, when selecting the best solutions, of course preference has been given to completely correct solutions. This leaves us with just two submissions, from Zhening Li and from  Eddie Chen. Out of those two, the solution of Zhening Li is more accurate as it further improves the accuracy by considering image charges induced on the spheres (just a small comment to his solution: while dipole radiation does carry away a small fraction of energy, it is very weak due to the smallness of the  acceleration; the main factor leading to the decay of oscillations is the Ohmic loss in the rod when charge is flowing from one ball to another). Furthermore, it is a very nicely written solution with detailed explanations, typeset in LaTeX. Therefore, Zhening Li will receive 60% of the bonus while  Eddie Chen will get 40%.

Apart from these two, there are two more solutions well worth publishing:
Vlad-Ștefan Oros has also nice detailed explanations and estimates the charge relaxation time which is an important parameter of the problem;
Nikita Semenin who has written and analyzed the full set of differential equations describing the intermediate dynamics of the system.

Final results for Problem 1

Pre-university students

First nameSurnameCountrySchoolDateTimeScore
ZheningLiCanadaSir John A. Macdonald Secondary School29.12.204:103.906
EddieChenUnited StatesWest-Windsor Plainsboro High School North01.01.213:252.907
Vlad-ȘtefanOrosRomaniaGrigore Moisil Informatics High School27.12.2016:222.853
OliwierUrbańskiPolandLiceum Ogólnokształcące nr 7 w Poznaniu27.12.2018:052.358
AntoniaGhitaRomaniaInternational Computer High School of Bucharest03.01.2111:491.772
JoshuaTeoSingaporeNUS High School04.01.215:401.611
MinhTrang DaoVietNamHus highschool for gifted students15.01.219:111.318
AnastasiaPozharkovaRussiaMBOU “Gymnasium 91 named after M. V. Lomonosov”16.01.217:271.078
Caio AugustoSiqueira da SilvaBrazilColégio Objetivo Integrado23.01.215:560.968
Manh QuanNguyenVietnamHanoi – Amsterdam High School for the Gifted23.01.2117:210.880
LotusChenChinaNo.2 High School Shijiazhuang24.01.213:560.800
BalázsKovácsHungaryHatvani Bajza József Gimnázium29.01.2119:340.700
Minh HoàngVietNamHUS High School for Gifted Students01.02.2114:190.600
Jianzheng   DengChinaShenzhen Senior High School02.02.216:290.600
ThanadisCharoenrujijinThailandSuankularb Wittayalai School04.02.218:040.600
Huy PhuongDangVietNamHigh School for Gifted Students07.02.2114:410.600
Sebastián AndrésArévalo AguirreEl SalvadorInstituto Emiliani13.02.210:020.600
RailKhashaevUzbekistanSecondary school N7131.01.2117:580.570
AlexandarRoussevBulgariaFirst Language School01.02.217:050.570
ViníciusFerreira RodriguesBrazilColégio Master06.02.211:380.540
DušanBegušSerbiaMathematical Grammar School01.02.210:470.437

University students

First nameSurnameCountryUniversityDateTimeScore
ElioMoreauItalyÉcole Polytechnique Fédérale de Lausanne30.12.2019:202.594
NikitaSemeninRussiaMoscow Institute of Physics and Technology08.01.2119:402.594
BatuhanKeskinTurkeyBoğazici University12.01.2122:051.754
YuechenZhuChinaPeking University11.01.215:471.742
TevžLotričSloveniaUniversity of Oxford16.01.2121:511.594
PieterVan SteenweghenBelgiumImperial College London24.01.212:231.288
QianLinChinaUniversity of Oxford24.01.2119:550.974
NguyenTanVietNamThe Hong Kong University of Science and Technology02.02.2115:080.799
RicardsKnipsisLatviaUniversity of Manchester11.02.2116:550.726
HuiyuanWangChinaUniversity of Cambridge15.02.214:260.627

Participating countries: Algeria, Azerbaijan, Australia, Bangladesh, Belarus, Belgium, Bosnia and Herzegovina, Bolivia, Brazil, Bulgaria, Cambodia, Canada, China, Croatia, Czechia, Egypt, El Salvador, Estonia, Finland, Georgia, Germany, Greece, Hungary, India, Indonesia, Iran, Israel, Italy, Japan, Kazakhstan, Kenya, Korea, Kyrgyzstan, Latvia, Lebanon, Lithuania, Macedonia, Malaysia, Mexico, Moldova, Mongolia, Nepal, Nigeria, North Macedonia, Pakistan, Peru, Philippines, Poland, Romania, Russia, Saudi Arabia, Serbia, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Syria, Taiwan, Thailand, Turkey, Turkmenistan, United Arab Emirates, United Kingdom, United States, Uzbekistan, Vietnam.