An infinitely long cylindrical conductor of radius a is plac

An infinitely long cylindrical conductor of radius a is placed along the z-axis. If the current density is J = J_0/rho z A/m^2 where J_0 is a constant, find H everywhere.

Solution

Current I uniformly flowing in cylinder current density j=i/a^{2 z^. (Inside wire). Solution independent of phi and z. Right hand rule then tell us H(r,phi,z) =H(r) phi, Ampere curve will be a circle of radius, dl=r,d,phi. Then H dl=2r H(r).}