Power-law poloidal field near a disk surface
= Power-law poloidal field near a disk surface
If $\Psi(R,0)=\Psi_1+\Psi_0(R/R_0)^\delta$ and the surface inclination to the vertical is a radius-independent $\alpha$, then $B_z=\delta\Psi_0R^{\delta-2}/R_0^\delta$ and $B_R=B_z\tan\alpha$. The <solenoidal vector field> condition gives
$$
\left.\partial_zB_z\right|_{0}=-\frac{\delta-1}{R}B_z(R,0)\tan\alpha.
$$
The constant offset in the <poloidal magnetic flux function> has no effect on the <magnetic field>.