(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A plane wave is incident at 70˚ to surface normal traveling within a medium with relative permittivity = 4, striking the boundary with air. Where is the nearest magnetic field max. to the boundary in the initial medium? Find the 1/e penetration depth of the evanescent wave.

2. Relevant equations

No equations are given, but i've been using:

θC= sin-1(εr2/ εr1)^.5

3. The attempt at a solution

For the second part, i said that in the air, Et and Ht vary with the factor: exp(-α_{2}z)exp(-jβ_{2x}x), where

α_{2}= β_{2}(εr1/ εr2*sin2θi-1)^.5 = 1.59β2 the 1/e penetration distance is then just

z = 1/(1.59β2) = .628β2

The first part, however, is where I am having my main difficulty. I think I know how to do it were this to be a plane wave incident on a conductor, but I am not sure if I can use the same logic for the air interface given that I don't think I can assume that E = 0 at the boundary. ( for a conductor, i've been able to solve for H for a TE wave being H_{1}=2*E_{i0}/Z_{1}*cos(β_{1}zcosθ_{i})*exp(-jβ_{1}xsinθ_{i})

from here I would just find where β_{1}zcosθ_{i}= 0 and that would give the max. Does this still work for an air incidence though? And is there any max for a TM wave?

Any help would be greatly appreciated! Thanks!

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# - Plane Wave Total Internal Reflection Problem

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