A plane electromagnetic wave of frequency ν=10 MHz propagates in a poorly conducting medium with conductivity σ=10 mS/m and relative permittivity εᵣ=9. Find the ratio of amplitudes of conduction-current density to displacement-current density, rounded to the nearest integer.
Physics · Electromagnetic wave
JEE Mains Advanced

Question

A plane electromagnetic wave of frequency ν=10 MHz propagates in a poorly conducting medium with conductivity σ=10 mS/m and relative permittivity εᵣ=9. Find the ratio of amplitudes of conduction-current density to displacement-current density, rounded to the nearest integer.

Physics · Electromagnetic wave

G1 Physics · Accepted Answer

The conduction-current-density amplitude is σE₀, while the displacement-current-density amplitude is ωεE₀. Their ratio is σ/(ωε)=σ/(ωε₀εᵣ). With σ=0.01 S m⁻¹, ω=2π×10⁷ rad s⁻¹ and εᵣ=9, the ratio is approximately 2. Hence the answer is 2.