Sea water at frequency ν = 4 × 108 Hz has permittivity ε ≈ 80 εo, V permeability µ ≈ µo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source V(t) = Vo sin (2π νt). What fraction of the conduction current density is the displacement current density? Fig. 8.1 8.30 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 sˆ the wire inside the cable is E (s,t ) = µo I o νcos(2πνt ) In k. a
This question refers to a figure in the original PDF.
- (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 dispalcement current I od .