Ncert Exercises & Solutions

A long straight cable of length l is placed symmetrically along the z-axis and has radius a(<<l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I (t) = I_{o} \sin (2 πνt)$ 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:

$E (s, t) = μ_{0} I_{0} νcos (2 πνt) \ln (\frac{s}{a}) \hat{k} .$

(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 $I^{d} .$
(iii) Compare the conduction current $I_{0}$ with the displacement current $I_{0}^{d} .$

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