How to calculate the axial components for a helix?

[needphyshelpalways]

Homework Statement

Calculate the axial component of the vector potential A_vector at the center of a helix of 2N turns, of radius R , and of the length 2H, carrying a current I . (Need to calculate only the axial component of the vector potential, and only at the origin.)
Then show that the result (for the axial component of the vector potential at the origin) is the same as that for a single wire of length 2H along the side of the helix that carries a current I . Why is this so?

Relevant Equations

A(r) = (mu/4pi)integral{(J(r)/r}dtau
B = gradient crossed with A

I attempted to use the relation that B = gradient crossed with A; however, I'm strguggling with how to setup the question. I think that alternatively the problem can be solved using the Poisson equation that A(r) = (mu/4pi)integral{(J(r)/r}dtau; however, here to I am struggling with the setup.

 

[BvU]

Hello needy, ##\qquad## ##\qquad## !

I attempted to use the relation that B = gradient crossed with A

Does that mean you already have A ? Probably not.

You only need the ##z##-component anyway. Can you write the integral a bit clearer ? In particular: what is ##{\mathrm d}\tau## ?

I am struggling with the setup

Well, start with making a good choice of your coordinate system. Any ideas ?