P. 4271. There is a pair of parallel, horizontal, conducting rails in uniform vertically downward magnetic field of induction B=0.5 T. The two rails are at a distance of =10 cm and they are connected to a rechargeable battery of potential difference U0=12 V. A metal rod of mass m=50 g, and of resistance R=2 , is placed onto the rails, perpendicularly to them. The coefficient of friction between the rod and the rails is =0.3.
a) What is the initial acceleration of the rod when switch K is closed?
b) What would the final speed of the rod be if the rails are very long?
c) Estimate, (try to give a precise estimation) the covered distance, and the time during which the speed of the rod increases from to .
Deadline expired on 11 October 2010.
Google Translation (Sorry, the solution is published in Hungarian only.)
Megoldás. \(\displaystyle a)\) A kezdeti gyorsulás \(\displaystyle 3~m/s^2\).
\(\displaystyle b)\) A rúd végsebessége 120 m/s lehet.
\(\displaystyle c)\) 34 ms alatt 14 cm-es úton gyorsul fel a rúd 4,0 m/s-ról 4,1 m/s sebességre.