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