Physics Cup – TalTech 2025 – Problem 1

By Jaan Kalda (TalTech).

The center of a non-magnetic metal ball with radius R is at the origin; the ball is in a homogeneous magnetic field B that is parallel to the x-axis. The ball rotates with an angular speed \omega around the x-axis. At x=L, y=z=0, there is another identical metal ball that does not rotate. Find the interaction force between the two balls, assuming that L\gg R and R\ll \sqrt{\rho/\mu\omega}, where \rho denotes the ball’s resistivity and \mu is the permeability.

Please submit the solution of this problem via e-mail to physcs.cup@gmail.com. After the publication of the first hint, the base score is reduced to 0.9 pts. For full regulations, see the “Participate” tab.