I can't remember the exact maths, but in he near field region, whether the electric or magnetic field is stronger, depends on whether it's a rod or loop.
In the far field region, both the magnetic fields decay at the same rate, in accordance with inverse square law, so 1/d
2 makes sense.
https://en.wikipedia.org/wiki/Inverse-square_lawIn the near field region, the stronger field, whether it be magnetic, or electric, decays at a faster rate of 1/d
3 and the weaker one decays at 1/d
2.