Show that the dimensions of the displacement current `(epsilon_0(d Phi_E)/dt)` are that of an electric current.

A long straight cable of length l is placed symmetrically along z-axis and has radius a(ltlt l). The cable consists of a thin wire and a co- axial conducting tube. An alternating current I(t) = I_(0) " sin " (2pi vt) . Flows down the central thin wire and returns along the co-axial conducting tube. the induced electric at a distance s from the wire inside the cable is E(s ,t) =mu_(0) I_(0) v " cos "(2pivt) In ((s)/(a)) hatk . (i) Calculate the displacement current density inside the cable. (ii) Integrate the displacement current density across the cross- section of the cable to find the total displacement current I^(d) . (iii) compare the conduction current I_(0) with the displacement current I_(0)^(d) .