How to Calculate the Magnetic and Electric Field

[Philosophaie]

Could someone show me a real world example of how to calculate the Magnetic and Electric Field around the Sun or a Planet.
$$\vec{B} = \nabla * \vec{A} = (B_x, B_y,B_z)$$
$$\vec{E} = -\nabla*\phi-\frac{\partial \vec{A}}{\partial t} = (E_x,E_y,E_z)$$

 

[UltrafastPED]

For these equations you must first know the value of the vector potential, $$\vec{A}$$, and the electric potential, $$\phi$$.

 

[Philosophaie]

How do you solve for $\vec{A}$ and $\phi$ for a planet or star acting like a dipole or current loop? For the sun the equations only are valid every 11 years or so because the polarity reverses. Also the Earth does not have a true North North Pole it is somewhere in Siberia.

 

[UltrafastPED]

"Mathematical Modeling of Earth’s Magnetic Field":
http://hanspeterschaub.info/Papers/UnderGradStudents/MagneticField.pdf

 

[Philosophaie]

Does anyone know where there is a list by date of Gaussian coefficients from the IAGA and IGRF(more recent then 2000).
They look like this $g^m_n$ and $h^m_n$

 

[UltrafastPED]

See footnote 2; but NASA is shutdown this week.