Yeah, the current magnetization of the sphere carries all the history of the magnetic fields it's been in in its value. The hysteresis in the material only mea

Yeah, the current magnetization of the sphere carries all the history of the magnetic fields it's been in in its value. The hysteresis in the material only means that if you apply 1T to it to magnetise (supposing the ball starts with zero magnetisation) it and then apply 0T to demagnetise it, the remanent field in the ball would be like 0.4T due to hystetesis, you need to apply something like -0.4T to leave it as it started.