How does a good conductor affect an electromagnetic wave, and what is the formula for skin depth?

How does a good conductor affect an electromagnetic wave, and what is the formula for skin depth?

• A. Waves propagate with no attenuation; δ = 1/√(μ σ ω)
• B. Waves are strongly attenuated; δ = sqrt(2/(μ σ ω))
• C. Waves amplify; δ = μ σ ω
• D. Waves reflect completely; δ = √(ε/μ)

Answer: (B)

When a good conductor is exposed to an oscillating electromagnetic field, currents flow near the surface and dissipate energy as heat. These currents oppose the changing field, so the wave loses amplitude as it penetrates the material. The depth at which the wave amplitude falls to 1/e of its surface value is called the skin depth, δ. In a good conductor, solving Maxwell’s equations for a plane wave gives a complex propagation constant whose magnitude leads to α ≈ β ≈ sqrt(ω μ σ / 2), where α is the attenuation constant. The skin depth is the reciprocal of that attenuation, so δ = 1/α = sqrt(2/(μ σ ω)). This shows that higher conductivity, higher frequency, or greater permeability shrink the skin depth and cause stronger attenuation of the wave as it goes in. That is why a good conductor causes strong attenuation of the wave. The other formulas either miss the correct factors or describe other behaviors (like amplification or complete reflection) that don’t match how skin depth depends on μ, σ, and ω.

When a good conductor is exposed to an oscillating electromagnetic field, currents flow near the surface and dissipate energy as heat. These currents oppose the changing field, so the wave loses amplitude as it penetrates the material. The depth at which the wave amplitude falls to 1/e of its surface value is called the skin depth, δ. In a good conductor, solving Maxwell’s equations for a plane wave gives a complex propagation constant whose magnitude leads to α ≈ β ≈ sqrt(ω μ σ / 2), where α is the attenuation constant. The skin depth is the reciprocal of that attenuation, so δ = 1/α = sqrt(2/(μ σ ω)). This shows that higher conductivity, higher frequency, or greater permeability shrink the skin depth and cause stronger attenuation of the wave as it goes in.

That is why a good conductor causes strong attenuation of the wave. The other formulas either miss the correct factors or describe other behaviors (like amplification or complete reflection) that don’t match how skin depth depends on μ, σ, and ω.