Problem P. 3800. (April 2005)
P. 3800. A metal ring having three metallic spokes of lengths r=0.2 m is in a vertical plane and can spin around a fixed horizontal axis in a homogeneous magnetic field of a magnetic induction of B=0.5 T. The lines of magnetic field are perpendicular to the plane of the metal ring. Between the axis of the metal ring and its perimeter we connect a consumer of a resistance of 0.15 with the help of two sliding contacts. We fix a thread of negligible mass to the rim of the ring and wind it several times around the ring and to its end we fix a body of a mass of 20 g. At a given moment we release the body of mass m. The friction is negligible everywhere, the resistance of the ring, the spokes and the connected wiring is also negligible.
a) What is the torque exerted on the ring with the spokes by the magnetic forces when the body of mass m is moving with a constant velocity?
b) What current is flowing through the consumer when the velocity of the body of mass m is 3 m/s?
c) What is the highest velocity of the body of mass m?
Deadline expired on May 11, 2005.
36 students sent a solution. 4 points: Csire Gábor, Darázs Zoltán, Deák 666 Áron, Domonkos Tamás, Engedy Balázs, Gondán László, Gyenis András, Hevesi Péter, Hotzi Bernadette, Kovács 216 Krisztina, Lapis Leonárd, Legoza József, Nagy 317 Péter, Nagy 569 István, Széchenyi Gábor, Szolnoki Lénárd. 3 points: Demeter Dániel, Hagymási Imre, Pál Tamás, Roósz Gergő, Sikó Lóránt. 2 points: 10 students. 1 point: 5 students.