Seawater at frequency v = 4 108 Hz has permittivity ε = 80 ε0,

Question:

Seawater at frequency v = 4 108 Hz has permittivity ε = 80 ε0, permeability μ= μ0 and resistivity ρ = 0.25 Ωm. Imagine a parallel plate capacitor immersed in seawater and driven by an alternating voltage source V(t) = V0 sin (2πvt). What fraction of the conduction current density is the displacement current density?

Solution:

The separation between the plates of the capacitor is V(t) = V0 sin (2πvt)

Ohm’s law for the conduction of current density J0c = V0/ρd

The displacement current density is Jod = 2πvεV0/d

The fraction of the conduction of current density and the displacement density = J0d/J0c = 4/9

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