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Question

When a ball made of uniform magnetic is introduced into an external uniform magnetic field with induction B0, it gets uniformly magnetized. Find the magnetic induction B inside the ball with permeability μ; recall that the magnetic field inside a uniformly magnetized ball is uniform and its strength is equal to H=J3, where J is the magnetization.

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Solution

We use the fact that within an isolated uniformly magnetized ball,
H=J3, B=2μ0J3, where J is the magnetization vector. Then in a uniform magnetic field with induction B0, we have by superposition,
Bin=B0+2μ0J3, Hin=B0μ0J3
or, Bin+2μ0Hin=3B0
also, Bin=μμ0Hin
Thus, Hin=3B0μ0(μ+2) and Bin=3μB0μ+2

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