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I have had this question since I was in college physics, but never could figure out how to express it. Well, now I think I have it.

Let's imagine two scenarios A and B. Both scenarios start with two non-magnetized iron bars. In scenario A, the iron bars are 0.1 m apart. In scenario B, they are 0.5 m apart. In both scenarios, one bar is magnetized over time to the same strength.

The question is in two parts:

  1. do the potential energies due to magnetism differ in the two scenarios?
  2. does the energy required to magnetize the iron bar differ in the two scenarios?

The question relates to how to account for the difference in potential energy. My reasoning is that the only place it can be drawn from is the energy required to magnetize the bar. Is this reasoning correct?

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First, if the magnetic strength of both the iron-bars after magnetizing are same. The system with largest distance takes more energy to get magnetized.

Second, if the amount of energy supplied to both the iron bars are same, the system with least distance will get more magnetized.

BTW, in the above cases, the energy supply (Magnetic Field) is constant, the source and the two iron bars form an isosceles triangle with the distance from iron bars to the source is same in all cases.

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