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Magnetostatics - Magnetic Vector Potential - Multipole Expansion of the Vector Potential

5 important questions on Magnetostatics - Magnetic Vector Potential - Multipole Expansion of the Vector Potential

How do we call the first term in multipole exoansion? What is its integral?

It is the monople term, the secon term is the dipole term and re third quadrupole term.

It term is always zero, for the integral is just a totl vector displacement around a closed loop .

This also means that there are no magnetic monopoles in natue. (bc divergence is zero). Therefore, ye dominant term is the dipole

How does the dipole vector potential look like?

Current is replacesd wiyj an angular fraction

How do we achieve the magnetic dipole moment?

We achieve it from the vector potential. In which a is the vector are of the loop . If the loop is flat a is the ordinary area.

The magnetic dippole moment also has a superposition.

Can we get a pure dipole for which the dipole vector potential is exact?

It can e done if we take an infitesmall loop at the origin, but to keep te dipole moment finite the current has to go up to infinity, with m=Ia held fixed.

How do we calculate the field of a perfect dipole?

It can also be noticed the pure dipole is identical to the one of an electric dipole. However, the field of a physical magnetic dipole looks quitedifferent from the electric counterpart