Question

Consider a cylindrical wire of radius R (indefinitely long) that carries a total steady current I such that there is a constant current density j across the profile of the wire (for the first part of this task, consider just a current density in vacuum)

a) in order to calculate the magnetic induction it is suitable to work in cylindrical coordinates. Considering Boundary conditions at ρ→∞, the magnetic induction ca be written as B=B_ρ (ρ,φ,z) e_ ρ + B_ φ(ρ,φ,z)e_ φ Use the symmetry of the infinitely long cylindrical wire(and the corresponding current density) to simplify this ansatz for the magnetic induction.

b) use maxwell´s equation (no magnetic monopoles) to show that there is no component of the magnetic induction in the radial direction. Hint: use Gauss theorem together with a cylindrical volume.

c) How does the result of your calculation change if only the conductor of the wire has a magnetic susceptiblity χ>0? Hint: use the material equations and the equation for linear media.

Please answer (b) and (c) only. Answers to the same problem have been posted but please do not copy them. Thank you very much in advance.

Answer 1