If the sun didn’t rotate, then the frozen-in magnetic field would be carried out radially with the solar wind (v = 440 km/s on average). Instead, the sun’s rotation (ω = 2.87 x 10^-6 rad/s) drags the magnetic field configuration into a Parker Spiral.

The angle between the radial flow and the spiral can be found with simple trigonometry.

\tan{θ} = \frac{rω}{v}

where the radial component of the magnetic field at some distance from the sun’s center can be found through the conservation of magnetic flux.

B_rA_r = B₀A₀

B_r(4πr²) = B₀(4πR²)

B_r = B₀[\frac{R}{r}]²

where R is the original distance from the origin (in this case, the radius of the sun).

As the sun rotates, it develops the longitudinal (a.k.a. azimuthal) component B_φ, described by the right triangle such that

\tan{θ} = \frac{-B_{φ}}{B_{r}} = \frac{rω}{v}

B_{φ} = -B_{0}[\frac{R^2}{r}][\frac{ω}{v}]