Suppose we have a cylindrical wire of radius a carrying a current I. If the current is uniformly distributed over the surface of the wire, the magnetic field inside is zero.
We can prove that easily using Ampere's law. However, when I try to picture it in my head I can't see why.
I imagine that the cylinder is made up of infinite straight wires , each of them contributing to the total magnetic field by $B=\frac{μ_0I}{2\pi a}$ . If we had two straight wires it's obvious that exactly between them the B fields are cancelled out.
With that in mind it's easy to see that in the middle of the cylinder every B component is cancelled by its symmetrical one. What about the rest points? It seems that one side is more powerful.