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

GATE-2012

29. Given the frequency of an electromagnetic wave to be 1KHz and ground conductivity to be 10 S/m, calculate the Skin depth.( Give answer in nearest integer , in meters).

A) 2                 B) 3           C) 5                      D) 8
  

Solution:

In Electromagnetic method,

Skin depth: If an electromagnetic wave hits a 

conductor the wave will attenuate as it penetrates 

the conductor with a characteristic distance, called

 the 'Skin depth(d)'

The Skin depth depends not only on the conductivity 

and Permittivity, but also on the frequency of the 

incident radiation. 

d= 503.8 √(ρ/f) ------------(1)

ρ= resistivity (Ω m)

f= frequency (Hz) = 1000 Hz

σ = 1/ ρ = conductivity (S/m) = 10 S/m

d= 503.8 √( 1/ (σ f))

  = 503.8 √ ( 1/ (10* 1000))

  = 503.8/ 100

Skin depth d= 5.038 m