Mathematical and Physical Journal
for High Schools
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# Problem P. 4701. (January 2015)

P. 4701. Small balls of charge $\displaystyle Q$ are attached to the points $\displaystyle P_1$ and $\displaystyle P_2$ of a ring, made of some insulating material, moving in a vertical plane, such that $\displaystyle \alpha=60^\circ$. The ring is in a homogeneous magnetic field of induction $\displaystyle B$, the magnetic field lines are perpendicular to the plane of the ring. The ring is moved such that it rolls without skidding on the horizontal surface which is also made from some insulating material. The speed of the centre of the ring is $\displaystyle v_0$.

$\displaystyle a)$ What is the magnitude of the magnetic force exerted on each charge at the position shown in the figure?

$\displaystyle b)$ At which positions of the ring will the torque of the sum of the magnetic forces calculated about the centre of the ring be zero? Considering only these positions, in which case will the force exerted by the magnetic field on the ring be the greatest and what is this greatest force?

$\displaystyle c)$ Determine the intersection of the lines of action of the magnetic forces.

(5 pont)

Deadline expired on February 10, 2015.

### Statistics:

 36 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Berta Dénes, Blum Balázs, Bugár 123 Dávid, Büki Máté, Csathó Botond, Forrai Botond, Fülöp Erik, Gróf Tamás, Holczer András, Iván Balázs, Jakus Balázs István, Kasza Bence, Kovács Péter Tamás, Lőrincz Zoltán, Marosvári Kristóf, Molnár 157 Marcell, Németh Flóra Boróka, Öreg Botond, Pázmán Előd, Sal Kristóf, Szántó Benedek, Varju Ákos, Wiandt Péter. 4 points: Bekes Nándor, Fehér Balázs, Fekete Panna, Kaposvári Péter, Körmöczi Dávid, Olosz Balázs, Szabó 199 Márton, Szász Norbert Csaba. 3 points: 3 students.

Problems in Physics of KöMaL, January 2015