Why Is the Magnetic Vector Potential Azimuthal Inside an Infinite Solenoid?

[pardesi]

Why is the magnetic vector potential of a point inside a infinite soleniod azimuthal assuming the axis of solenoid is the z axis.
Problem is the formulae $A(\vec r)=\int_{v} \frac {\vec J(\vec r^{'})}{r} d\tau$ doesn't hold any more due to the infinite extent of the current

 

[Crosson]

When you say "why is" I assume you mean "what is", and A is simple to find in this case because you can find B using the integral form of ampere's law and then guess A by looking at B = Curl(A).