 Mathematical and Physical Journal
for High Schools
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# Problem P. 4839. (April 2016)

P. 4839. A solenoid is made by winding tightly (in one layer) a piece of enamelled wire of resistivity $\displaystyle \varrho$, and of radius $\displaystyle r\ll R$ around an insulating cylinder of length $\displaystyle \ell$ and of radius $\displaystyle R\ll \ell$. The solenoid is connected to a voltage supply of voltage $\displaystyle U$. To what power of the radius $\displaystyle r$ are the following quantities proportional?

$\displaystyle a)$ The current in the wire;

$\displaystyle b)$ the self-inductance of the solenoid;

$\displaystyle c)$ the magnitude of the magnetic induction at the geometric centre of the solenoid.

(4 pont)

Deadline expired on May 10, 2016.

### Statistics:

 49 students sent a solution. 4 points: Bartók Imre, Bekes Nándor, Blum Balázs, Csenger Géza, Csire Roland, Csorba Benjámin, Csuha Boglárka, Elek Péter, Fajszi Bulcsú, Farkas Domonkos, Gémes Antal, Iván Balázs, Kavas Katalin, Körmöczi Dávid, Mándoki László, Marozsák Tóbiás , Nagy Nándor, Németh 777 Róbert, Németh Flóra Boróka, Olosz Adél, Pataki 245 Attila, Pázmán Előd, Sallai Krisztina, Szántó Benedek, Szőke Dániel, Tófalusi Ádám, Tomcsányi Gergely, Topa Lukács, Varga-Umbrich Eszter, Wiandt Péter, Zöllner András. 3 points: Ardai István Tamás, Bukor Benedek, Jakus Balázs István, Kluèka Vivien, Molnár Mátyás, Sal Kristóf. 2 points: 3 students. 1 point: 6 students. 0 point: 3 students.

Problems in Physics of KöMaL, April 2016