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The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24o
Que: The skin depth is
  • a)
    2.52 m
  • b)
    5.05 m
  • c)
    8.46 m
  • d)
    4.23 m
Correct answer is option 'B'. Can you explain this answer?
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Given data:
Frequency of wave, f = 10 MHz
Attenuation constant, α = 0.18 m⁻¹
Phase difference, φ = 24°

To find: Skin depth

Formula used:
Attenuation constant, α = √(ωμσ/2)
Phase difference, φ = arctan(2ωμδ)

where,
ω = 2πf is the angular frequency
μ = permeability of the medium
σ = conductivity of the medium
δ = skin depth

Calculation:
ω = 2πf = 2π × 10^7 rad/s

Let's assume the permeability of the medium is the same as the permeability of free space, μ₀ = 4π × 10⁻⁷ H/m.

Using the formula for attenuation constant, we get:
α = √(ωμσ/2)
0.18 = √(ωμ₀σ/2)
σ = (2α/ωμ₀)² = (2 × 0.18 / (2π × 10^7 × 4π × 10⁻⁷))² = 3.239 × 10⁷ S/m

Using the formula for phase difference, we get:
φ = arctan(2ωμδ)
tan(φ) = 2ωμδ
δ = (2ωμtan(φ))⁻¹ = (2 × 2π × 10^7 × 4π × 10⁻⁷ × tan(24))⁻¹ = 5.05 m

Therefore, the skin depth of the medium is 5.05 m.

Answer: (B) 5.05 m
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The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The skin depth isa)2.52 mb)5.05 mc)8.46 md)4.23 mCorrect answer is option 'B'. Can you explain this answer?
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