The magnetic vector potential contributed by a length with current running through it is
What is the magnetic vector potential a distance from a long straight current element?
Assume the wire is placed on the z-axis. Hence the distance from a differential element to a point in space is
Now it is necessary to integrate over the length of the rod. Since the rod is arbitrarily said to be on the z-axis, it can be said, for simplicity, to extend from to This simply requires multiplying by 2. Also, use the substitution