Introduction to Electrodynamics · Problem 7.40

Conservation Laws — David J. Griffiths

Physics · displacement-current-in-matter

Problem

Sea water at frequency ν=4×108\nu = 4 \times 10^8 Hz has permittivity ϵ=81ϵ0\epsilon = 81\epsilon_0, permeability μ=μ0\mu = \mu_0, and resistivity ρ=0.23 Ω⋅m\rho = 0.23\ \Omega \cdot \text{m}. What is the ratio of conduction current to displacement current? [Hint: Consider a parallel-plate capacitor immersed in sea water and driven by a voltage V0cos⁡(2πνt)V_0 \cos(2\pi\nu t).]

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