Let a ring of radius a carry a current I, and set up cylindrical coordinates 
. Let 
be the angle between the z axis and the observer.
On-axis, in cgs
where c is the speed of light, so
In MKS,
where
is the permeability of free space, so
Off-axis in MKS, the magnetic vector potential is
where
and K(k) and E(k) are complete elliptic integrals of the first and second kind with modulus k.
. Let be the angle between the z axis and the observer.On-axis, in cgs
(1)
where c is the speed of light, so
(2)
In MKS,
(3)
where
is the permeability of free space, so (4)
Off-axis in MKS, the magnetic vector potential is
(5)
where
(6)
and K(k) and E(k) are complete elliptic integrals of the first and second kind with modulus k.
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