1. The problem statement, all variables and given/known data A long, cylindrical conductor of radius R carries a current I. The current density, J, is not uniform and is given by the equation J = br, where b is a constant. Find an expression for the magnetic field magnitude B at distance r < R and at distance r > R. 2. Relevant equations I = ∫JxdA B= μI/(2pi*r) 3. The attempt at a solution So I think that I have this figured out, but it's an even numbered problem so I don't know if I'm correct. a) First finding I inside r I = ∫JxdA = ∫br2(pi)rdr = 2(pi)b∫r^2dr = 2/3(pi)br^3 when integrating from 0 to r So B = μI/(2(pi)r) = 2μ(pi)br^3/(6(pi)r) = μbr^2/3 b) First finding total I I = ∫JxdA = ∫br2(pi)rdr = 2(pi)b∫r^2dr = 2/3(pi)bR^3 when integrating from 0 to R so B = μI/(2(pi)r) = 2μ(pi)bR^3/(6(pi)r) = μbR^3/(3r) I'm pretty sure it's correct, but not entirely sure.