Physics Cup 2022 Problem 1

Physics

Problem

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?

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