The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization M\bf{M}. I would like to find the the magnetic field far above the plate. My expectation is that far above the plate, the field should approach the dipolar field which scales as 1/r31/r^3. However my numerical calculations are yielding 1/r41/r^4. I am using Jackson's book (3rd ed.) as a guide. I assume discontinuous magnetization at the surface so I can use Jackson's Eq. 5.100 which is the magnetic scalar potential: ΦM(x)=14π∮Sn′⋅M(x′)∣x−x′∣da′\Phi_M (\bf{x}) = \frac{1}{4 \pi} \oint_S \frac{\bf{n}' \cdot \bf{M}(\bf{x}')}{|\bf{x}-\bf{x}'|}da' assuming that the magnetization M(x′)\bf{M}(\bf{x}') is uniform within the volume. The top and bottom surfaces of the film will contribute to the potential. If I focus just on the top surface and assume a normalized magnetization M=Mz^\bf{M} = M \hat{z}: ΦM(x)=14π∮topM∣x−x′∣da′.\Phi_M (\bf{x}) = \frac{1}{4 \pi} \oint_{top} \frac{ M}{|\bf{x}-\bf{x}'|}da'. I do not see where to go from here or how the expected 1/r21/r^2 dependence will arise.