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Solved Problems-11

Problem-11
Assume a plane wave with E = 1 V/m and a frequency of 300 × 106 cps moving in free space, impinges on a thick copper plate located perpendicularly to the direction of propagation. Find
  1. E at the plane surface
  2. H at the same location
  3. δ, depth of penetration
  4. Conduction current density at the surface
  5. J, the conduction current density, at the depth of 10-2 mm
  6. Surface current density
  7. Surface impedance
  8. Power loss per square metre of surface area
Assume σ = 5.8 × 107 mho/m. ε = ε0, μ = μ0.
Solution
Given: Ei = 1 V/m, f = 300 × 106 cps

(a) Here, η1 = 377 Ω
 
∴ transmission coefficient is,
 
Description: 41471.png
 
(b)
Description: 41464.png
(c) Depth of penetration,
 
Description: 41457.png
 
(d) Conduction current density at the surface is,
 
Description: 41448.png
 
(e) At a distance x below the surface, the conduction current density is given as,
     Description: 41439.png
 
where, Description: 41431.png
 
Description: 41422.png
 
So, at a distance, x = 0.01 × 10-3 m, the conduction current density is,
 
Description: 41414.png
 
(f) According to the boundary condition, the surface current density is equal to the tangential component of the magnetic field. From the result of (b), we have the surface current density given as,
 
Description: 67619.png
 
(g) Surface impedance is given as,
 
Description: 67629.png
 
(h) Power loss per square metre of surface area is,
 
Description: 67637.png
 





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