Physics Cup – TalTech 2022 – Problem 1

By Jaan Kalda (TalTech).

A spherical ball of radius $R=1$cm 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, $T_1= 20^\circ$C, and $T_2= 120^\circ$C . Initially, the ball has been magnetized by putting it into a very strong homogeneous magnetic field (with $B\approx 3$T). Then, the external magnetic field is removed while the temperature of the ball is kept equal to $T_1= 20^\circ$C . After that, the ball is heated up to the temperature $T_2= 120^\circ$C . 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 physcs.cup@gmail.com. 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.