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Problem P. 4592. (December 2013)

P. 4592. There are two conducting wires of negligible resistances in a horizontal plane enclosing an angle of \alpha. A long enough rod of mass m is placed onto the wires, perpendicularly to the angle bisector of the angle between the wires at a distance of x0 from the intersection A of the two wires as shown in the figure. The resistance per unit length of the rod is r. The arrangement is put into uniform vertical magnetic field of magnetic induction B.

The rod is given an initial velocity of v0 in the direction of the angle bisector. The electrical contact between the wires and the rod is good, but the friction is negligible between them. Where will the rod stop?

(5 pont)

Deadline expired on January 10, 2014.


Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. \(\displaystyle x_\text{max}=\sqrt{x_0^2+\frac{mv_0r}{B^2{\rm tg}(\alpha/2)}}.\)


Statistics:

30 students sent a solution.
5 points:Antalicz Balázs, Asztalos Bogdán, Balogh Menyhért, Berta Dénes, Blum Balázs, Büki Máté, Csathó Botond, Dinev Georgi, Fehér Zsombor, Fekete Panna, Forrai Botond, Géczi Péter Attila, Holczer András, Horicsányi Attila, Janzer Barnabás, Juhász Péter, Olosz Balázs, Sági Olivér, Sal Kristóf, Sárvári Péter, Trócsányi Péter.
4 points:Kenderes Anett.
3 points:3 students.
2 points:5 students.

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