A hollow cone carries charge spread evenly across its surface. Spin it about the z-axis and every charge starts circling — moving charge is current, and current makes a magnetic field. Far above the cone, that field behaves like a single dipole.
Split the surface into thin horizontal bands. A band at height z has radius r = (R/h)·z and holds a slice of the total charge.
As the cone turns, every band's charge goes around once per revolution. That circulating charge is a current loop — a tiny magnetic dipole.
Sum every ring's dipole moment to get the cone's total moment m. From far away (z ≫ R, h) only this net dipole matters.
The whole problem reduces to finding the net dipole moment, then reading off the constant n. The z⁻³ falloff is the fingerprint of a dipole.