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- Why is the monopole term 0 in the multipole expansion for Magnetic Vector Potential A.

when you do a multipole expansion of the vector potential you get a monopole, dipole, quadrupole and so on terms. The monopole term for a current loop is μI/4πr*∫dl’ which goes to 0 as the integral is over a closed loop. I am kinda confused on that as evaulating the integral gives the arc length but it should go to 0. For example for a circular loop ∫dl’ just gives 2πr’ which is the circumference, not 0. dl’ in Spherical coordinates is <dr, rdθ, rsinθdφ> So if we take θ=π/2 and integrate dφ As the current is in the φ direction we end up with 2πr’. Could someone show how the integral goes to 0 like actually show rigorously by evaluating it and proving that it goes to 0 and explain any mistake I made in the integration.