A metal has uniform conductivity $\sigma$. A cylindrical wire with radius $a$ and length $l$ is manufactured from the metal. Show, using Maxwell's equations, that when a steady current $I$ flows along the wire the current density within the wire is uniform.

Deduce the electrical resistance of the wire and the rate of Ohmic dissipation within it.

Indicate briefly, and without detailed calculation, whether your results would be affected if the wire was not straight.