2. The current distribution of an infinite,wire can be described in cylindrical coordinates byJ = J(p) 2.longitudinally-uniform, and axially-symmetric(a) Show that. J = 0.(b) Considerations of longitudinal and axial symmetry require that the mag-netic field can only depend upon p, i.e. thatB(p) = Bp(p)ô + Bø(p) + B₂(p)2.Use Ampère's Law to determine B6 (p) in terms of I (p) = 2π J(p') p'dp'.(c) Use the Biot and Savart Law to show that Bp(p) = B₂ (p) = 0. Side note:it is pretty easy to show that B,(p) must be zero using Gauss's Law forB with a cylindrical volume. I am not aware of an "easy" way to seeB₂ (p) = 0 - not that it is very difficult using the Biot and Savart Law...(d) Use the integral form for the vector potential [Jackson, Eq. (5.32)] todetermine A for this current distribution. Hint: in order to deal withdivergent integrals, you may want to limit the current distribution to-L ≤ z ≤ L, determine A, adjust A by a constant (as one is allowed todo), and then take L→ ∞.(e) Verify that the A in part (d) reproduces the B found in parts (b) and (c)when the curl is taken.

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