Sea water at frequency v = 4 × 108 Hz has permittivity ε ≈ 80 ε o , 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 . What fraction of the conduction current density is the displacement current density?

Question

Philoid · Accepted Answer

Frequency, v=4×10⁸ Hz

Permittivity, ε = 80 ε₀

Permeability, μ=μ₀

Resistivity, ρ=0.25 Ωm

Voltage, V=V₀ sin (2πvt)

Calculation:

Assume that the separation between the plates of the capacitor is d and the applied voltage is, V=V₀ sin (2πvt)

The electric field is given by,

The conduction current density is given by,

The displacement current density is given by,

Thus, fraction of the conduction current density is the displacement current density is given by