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.

Answered: Image /qna-images/answer/68c1ce4b-189d-43ad-84b6-e6507f860fdc.jpg

2. The current distribution of an infinite, longitudinally-uniform, and axially-symmetric wire can be described in cylindrical coordinates by J = J(p) 2. (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. that B(p) = B₂(p)p+ 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 B.(o)= B.(p) = 0. Side note:

2. The current distribution of an infinite, longitudinally-uniform, and axially-symmetric wire can be described in cylindrical coordinates by J = J(p) 2. (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. that B(p) = B₂(p)p+ 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 B.(o)= B.(p) = 0. Side note: