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Results after Problem 6

The list of the contest leaders after the sixth problem:

Points   Name Country School Physics teacher
15,578   Szabó Attila Hungary Leőwey Klára High School, Pécs Simon Péter, Dr Kotek László
14,129   Nikita Sopenko Russia Lyceum No.14, Tambov Valeriy Vladimirovich Biryukov
9,8178   Lars Dehlwes Germany Ohm-Gymnasium Erlangen Martin Perleth
9,499   Ilie Popanu Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
8,856   Jakub Šafin Slovak Pavol Horov Secondary, Michalovce Jozef Smrek
6,9689   Ion Toloaca Moldova liceul "Mircea Eliade" Igor Iurevici Nemtov; Andrei Simboteanu
6,8933   Ivan Tadeu Ferreira Antunes Filho Brazil Colégio Objetivo, Lins, São Paulo  
6,4407   Dinis Cheian Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
6,203   Alexandra Vasileva Russia Lyceum "Second School", Moscow A.R. Zilberman, G.F. Lvovskaya, G.Z. Arabuly 
6,1968   Jakub Supeł  Poland 14th School of Stanisław Staszic, Warsaw Włodzimierz Zielicz
6,0844   Cristian Zanoci Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
5,8911   Papimeri Dumitru Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
5,6695   Brahim Saadi Algeria Preparatory School for Science & Technology of Annaba Derradji Nasreddine
5,5644   Kohei Kawabata Japan Nada High School  
4,7997   Nadezhda Vartanian Russia Smolensk Pedagogical Lyceum Mishchenko Andrei Anatolievich
3,7517   Luís Gustavo Lapinha Dalla Stella Brazil Colégio Integrado Objetivo, Barueri, Brazil Ronaldo Fogo
3,4205   Bharadwaj Rallabandi India Narayana Jr. College, Basheer Bagh, India Vyom Sekhar Singh
3,2075   Petar Tadic Montenegro Gimnazija ,,Stojan Cerovic" Niksic Ana Vujacic
2,5937   Mikhail Shirkin Russia Gymnasium of  Ramenskoye  Petrova Elena Georgyevna
2,374   Lorenzo Comoglio  Italy Liceo Scientifico del Cossatese e Valle Strona Chiara Bandini
2,2747   Kai-Chi Huang Taiwan Taipei Municipal Chien-Kuo High School Shun-Ju Liu
2,1862   Ng Fei Chong Malaysia SMJK Chung Ling, Penang  
2,1   Krzysztof Markiewicz Poland XIV Highschool in Warsaw Robert Stasiak
2   Jaan Toots Estonia Tallinn Secondary Science School Toomas Reimann
1,5449   Selver Pepić Bosnia-Herzegovina Fourth Gymnasium Ilidža, Sarajevo Rajfa Musemić
1,4641   Bruno Bento Barros de Araújo Brazil Ari de Sá Cavalcante Edney Melo
1,4641   Hideki Yukawa Japan Nada high school  
1,21   Midhul Varma India Vidyadham Junior, Hyderabad  Manikanta Kumar
1    Adrian Nugraha Utama Indonesia SMA Sutomo 1 Medan Manaek Nababan, Salim Sabtu
1   Teoh Yee Seng Malaysia SMJK HENG EE,Penang; SMJK CHUNG LING,Penang  
1   José Luciano de Morais Neto Brazil Colégio Ari de Sá Cavalcante Leonardo Bruno
1   Task Ohmori Japan Nada High School T.Hamaguchi
1   Sharad Mirani  India Prakash Higher Secondary School Ruchi Sadana, Sunil Sharma
1   Lev Ginzburg Russia Advanced Educational Scientific Center, MSU, Moscow I.V. Lukjanov, S.N. Oks
0,9801   Mekan Toyjanow Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
0,9   Jôhanes Sebástian Paiva Melo Brazil Colégio Ari de Sá Cavalcante Eduardo Kilder; Italo Reann
0,81   Andrew Zhao United States Webster Thomas High School Dykstra, William 
0,81   Meylis Malikov Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
0,81   Liara Guinsberg Brazil Colégio Integrado Objetivo, São Paulo, Brazil Ronaldo Fogo
0,792   Ulysse Lojkine  France Lycée Henri IV, Paris M. Lacas
0,72   Rajat Sharma India Pragati Vidya Peeth,Gwalior Mr. Rakesh Ranjan

 

Points for Problem No 6:

2,8531   Szabó Attila
2,5937   Nikita Sopenko
2,2747   Kai-Chi Huang
2,2295   Lars Dehlwes
1,7538   Kohei Kawabata
1,4641   Bruno Bento Barros de Araújo
1,331   Ilie Popanu
1,3045   Petar Tadic
1,284   Alexandra Vasileva
1,1556   Jakub Šafin
1,1   Ion Toloaca
1    Adrian Nugraha Utama
1   Jakub Supeł 
1   Cristian Zanoci
1   Nadezhda Vartanian
1   José Luciano de Morais Neto
0,9801   Selver Pepić
0,9   Dinis Cheian
0,9   Jôhanes Sebástian Paiva Melo
0,81   Ivan Tadeu Ferreira Antunes Filho
0,81   Andrew Zhao
0,5648   Ng Fei Chong
0,5134   Lorenzo Comoglio 

 

Correct solutions (ordered according to the arrival time; best solutions in bold):

1. Szabó Attila (Hungary)

2. Nikita Sopenko (Russia)

3. Lars Dehlwes (Germany)

4. Kohei Kawabata (Japan)

5. Kai-Chi Huang (Taiwan)

6. Petar Tadic (Montenegro)

7. Bruno Bento Barros de Araújo (Brazil)

8. Ilie Popanu (Moldova)

9. Selver Pepić (Bosnia-Herzegovina)

10. Ion Toloaca (Moldova)

11, Nadezhda Vartanian (Russia)

12. José Luciano de Morais Neto (Brazil)

13. Jakub Šafin (Slovak)

14. Ivan Tadeu Ferreira Antunes Filho (Brazil)

15. Jôhanes Sebástian Paiva Melo (Brazil)

16.  Adrian Nugraha Utama (Indonesia)

17. Andrew Zhao (United States)

18. Ng Fei Chong (Malaysia)

19. Jakub Supeł (Poland)

20. Alexandra Vasileva (Russia)

21. Lorenzo Comoglio (Italy)

22. Cristian Zanoci (Moldova)

23. Dinis Cheian (Moldova)

(The list is ordered according to the arrival time)

 

Overall number of registered participants: 258 from 44 countries.

—————-

The following hints were given for the last week. It is clear that the charges can be only on the surface of the metal: on the spherical part, and on the two adjacent surfaces of the plane cut (volume charges inside the metal would create an electric field therein). Note also that at each point of the cut, the charges at the two sides need to compensate each other (uncompensated charge would create an electric field in the metal near the cut). You need to figure out, how the charges need to be distributed on these surfaces to ensure that the field will be potential (whichever way an imaginary test charge moves from one piece of the sphere to another one, the work done by the electric field should remain the same). Also, the electric field created by the charges on the spherical surfaces should cancel out inside the region occupied by the metal.

The following methods can be useful: study the Gauss law for a small volume near the spherical surface to express the electric field outside the sphere via the surface charge density at that location; study the circulation theorem for a small contour near the surface (but outside the sphere): near the surface, the electric field is perpendicular to the surface (ie. radial), so that the tangential segments of the contour give no contribution to the circulation, which makes it possible to draw useful conclusions regarding the behaviour of the  radial  field (about the dependence on the tangential coordinate).


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