A straight, cylindrical wire lying along the x axis has a length L and a diameter d. It is made of a material described by Ohm's law with a resistivity rho. Assume potential V is maintained at the left end of the wire at x = 0. Also assume the potential is zero at x = L. In terms of L, d, V, rho, and physical constants, derive expressions for the following. (Use the following as necessary: L, d, V, rho, and π.)
(a) the electric field in the wire.
(b) the resistance of the wire.
(c) the electric current in the wire.
(d) the current density in the wire.
(e) Show that E = rho.J