stars are magnetic monopoles ??

[Widdekind]

The Vector Potential, generated by an individual charge, is [math]\vec{A_{q}} \approx \frac{q}{r} \times \vec{v}[/math]. And, the Dirac expression, for the Vector Potential [math]\vec{A}[/math], of a magnetic monopole, in spherical coordinates, is:

 

[math]\vec{A_{m}} \approx \frac{1}{r} \times tan \left( \frac{\theta}{2} \right) \hat{\phi}[/math]

(Jackson.

Classical Electro-Dynamics

, p. 290)

Thus, qualitatively, a spherical distribution of charged plasma, rotating differentially, with "slowly spinning poles" and a "fast rotating equator", would have an azimuthal plasma velocity profile, comparable to [math]\vec{v} \approx tan \left( \frac{\theta}{2} \right) \hat{\phi}[/math]. And, that description sounds strikingly similar to a star, e.g. our sun, whose magnetic field is quasi-radial, according to the Parker model:

 

Parker’s model explained that the solar wind, emanating from the equator, forms a spiral in the equatorial plane... This is called the Parker spiral...

 

At higher latitudes, the solar wind travels outward radially, making tighter and tighter spirals, until, ultimately, at the poles, the wind simply travels outwards in a straight vertical line.

Indeed, such a shear-inducing, differential azimuthal velocity field, sounds completely consistent, with our sun's tacho-cline:

 

The tachocline is the transition region of the Sun, between the radiative interior, and the differentially rotating outer convective zone... The convective exterior rotates as a normal fluid, with differential rotation, with the poles rotating slowly, and the equator rotating quickly. The radiative interior exhibits solid-body rotation... The rotation rate through the interior is roughly equal to the rotation rate at mid-latitudes, i.e. in-between the rate at the slow poles and the fast equator. Recent results from helioseismology indicate that the tachocline is located at a radius of [math]< 0.70 R_{\odot}[/math], with a thickness of [math]0.04 R_{\odot}[/math]. This would mean the area has a very large shear profile, which is one way that large scale magnetic fields can be formed.

Thus, solar-like differential rotation, of charged plasma:

 

is qualitatively consistent, with quasi-radial "mono-polar" magnetic fields: