How to Calculate the Magnetic and Electric Field

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Calculating the magnetic and electric fields around celestial bodies like the Sun or planets requires understanding vector potential (A) and electric potential (φ). The equations for magnetic (B) and electric (E) fields depend on these potentials and are particularly valid for the Sun every 11 years due to polarity reversals. For accurate modeling, one must consider the Earth's magnetic field, which does not have a true North Pole. Additionally, there is a request for a list of Gaussian coefficients from IAGA and IGRF, particularly post-2000. The discussion emphasizes the complexities of modeling these fields in real-world scenarios.
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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)
 
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For these equations you must first know the value of the vector potential, \vec{A}, and the electric potential, \phi.
 
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.
 
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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##
 
See footnote 2; but NASA is shutdown this week.
 

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