Just as ∆ ∙ B = 0 allows us to express B as the curl of a vector potential (B = ∆ x A), so ∆ ∙ A = 0 permits us to write A itself as the curl of a "higher" potential: A = ∆ x W. (And this hierarchy can be extended ad infinitum.)

(a) Find the general formula for W (as an integral over B), which holds when B → 0 at ∞.

(b) Determine W for the case of a uniform magnetic field B.

(c) Find W inside and outside an infinite solenoid.