Results after Problem 2

The list of the contest leaders after the second problem:

Points for Problem No 2:

Correct solutions (ordered according to the arrival time):

1. Szabó Attila (Hungary).

2. Ivan Tadeu Ferreira Antunes Filho (Brazil)

3. Nikita Sopenko (Russia)

4. Jakub Šafin (Slovak)

5. Lars Dehlwes (Germany)

6. Ilie Popanu (Moldova)

7. Brahim Saadi (Algeria)

8. Alexandra Vasileva (Russia)

9. Luís Gustavo Lapinha Dalla Stella (Brazil)

10. Papimeri Dumitru (Moldova)

11. Ion Toloaca (Moldova)

Overall number of registered particpants: 204 (from 38 countries).

During the first week, only one correct solution has been submitted (by Szabó Attila). So, the problem was judged to be very difficult, and after the first week, few hints were published:

"You need to understand how to calculate fields using the circulation theorem and Gauss law; relevant formulas (from the formula sheet) are IX-2, IX-3 and IX-6; I also recommend studying the formulae VIII-8, VIII-9, VIII-13, IX-27, IX-28, and IX-29. And finally – this is a common mistake – the inductance of a coil is not always multiplied by a factor of when you supply it with a ferromagnetic core (in fact, it is multiplied by  only for very specific cases); the inductance will depend on the geometry of the ferromagnetic!"

During the second week, two more correct solutions were received: by Ivan Tadeu Ferreira Antunes Filho and Nikita Sopenko. So, another hint was added:

"In particular, it would be helpful to study the magnetic field created by electric transformers with closed (for instance, toroidal) ferromagnetic cores; Wikipedia is not too useful (there is no calculation of B), except for the figure for leakage flux (which is small/negligible, if µ is large)."

During the first half of the third week, the correct solution of Jakub Šafin was received. After that, on 3rd Nov, another amendment to the hints was made, so that the final wording was as follows:

"you need to understand how to calculate fields using the circulation theorem and Gauss law; relevant formulae (from the formula sheet) are IX-2, IX-3 and IX-6; I also recommend studying the formulae VIII-8, VIII-9, VIII-13, IX-27, IX-28, and IX-29. In particular, it would be helpful to study the magnetic field created by electric transformers with closed (for instance, toroidal) ferromagnetic cores; suggested reading from Wikipedia: figure for leakage flux (which is small, if µ is large); how to deal with magnetic circuits. Please bear in mind that you are not supposed to copy directly formulae from the latter article, because the shape of our ferromagnetic brick differs from a simplified model of a closed-core transformer; instead, it should be considered as a reading which helps you understand, what is going on with the B-field in our case, and how to correctly apply the circulation theorem.

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Jaan Kalda – Academic Committee of IPhO-2012