Physics Cup – TalTech 2022 – Problem 1

By Jaan Kalda (TalTech).

A spherical ball of radius R=1cm is made from a NdFeB alloy. The figure below shows the left upper quadrant (H<0, B>0) of the hysteresis loop of this alloy for two temperatures, T_1= 20^\circC, and T_2= 120^\circC . Initially, the ball has been magnetized by putting it into a very strong homogeneous magnetic field (with B\approx 3T). Then, the external magnetic field is removed while the temperature of the ball is kept equal to T_1= 20^\circC . After that, the ball is heated up to the temperature T_2= 120^\circC . By how much did the magnetic dipole moment of the ball change due to heating?

Please submit the solution of this problem via e-mail to First hints will appear here on 28th November 2021 or on 5th December, depending on the number of correct solutions submitted during the first week. After the publication of the first hint, the base score is reduced to 0.9 pts. For full regulations, see the “Participate” tab. The intermediate results for the Problem 1 will be drawn after 13:00 GMT, 28th November 2021.