GATE-2018 (24) :Wyllie – Time average equation

 

63) An EM wave travels vertically downwards in a homogenous medium of 100 m skin depth. At a depth of 200 meters what is the amplitude of the EM wave measured as percent of wave amplitude at the earth’s surface?

(Thanks to Chandrasekhar, ANU)

Solution:

Given that the Skin depth = 100 m

                   Depth = 200 m

 The amplitude of an EM wave can be defined as

$A=A_{0}e^{-\beta z}$

 

$A=A_{0}e^{-\frac{z}{\delta}}$

 

$\frac{A}{A_{0}}= e^{-\frac{z}{\delta}}$

 

$\frac{A}{A_{0}}= e^{-\frac{200}{100}}$

 

$\frac{A}{A_{0}}= e^{-2}$

 

$\frac{A}{A_{0}}= 0.135$

 

$\frac{A}{A_{0}}= 13.5 $%

For more information regarding above terms please check this post:

GATE-2018 (gpsurya.blogspot.com)