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A long straight cable of length l is placed symmetrically along z-axis and has radius a(<<l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current I(t) = Io sin (2πνt) flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is E(s,t)=  μoIovcos (2πνt) In (s/a)k.

(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 Id.

(iii) Compare the conduction current I0 with the displacement current Ido .

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(i) Displacement curing density can be found from the relation

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