An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, σ = 10 mho/m. The ratio of maximum conducting current density to maximum displacement current density i $s _________.$
[Take 1/(4πε₀) = 9 × 10⁹ Nm²/C²]

Question

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, σ = 10 mho/m. The ratio of maximum conducting current density to maximum displacement current density i $s _________.$

[Take 1/(4πε₀) = 9 × 10⁹ Nm²/C²]

G1 Physics · Accepted Answer

The conduction current density is J(conduction) = σE. Therefore its maximum value is J(conduction,max) = σE₀. For the electromagnetic wave, E = E₀ sin(ωt - kx). The displacement current density is J(displacement) = ε₀ dE/dt. Therefore, J(displacement) = ε₀ωE₀ cos(ωt - kx), and its maximum value is J(displacement,max) = ε₀ωE₀. Hence, J(conduction,max)/J(displacement,max) = σ/(ε₀ω). Given, 1/(4πε₀) = 9 × 10⁹. Therefore, 1/ε₀ = 4π × 9 × 10⁹. Also, ω = 2πf = 2π × 100 × 10⁶. Thus, ratio = 10(4π × 9…

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, σ = 10 mho/m. The ratio of maximum conducting current density to maximum displacement current density i s _________. [Take 1/(4πε₀) = 9 × 10⁹ Nm²/C²]