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

CSIR-NET 2015

42. An electromagnetic wave at 100Hz can penetrate to a depth of 100m. Then, an electromagnetic wave of 400Hz will penetrate to a depth of

1) 2.5 m 

2) 50m 

3) 200m 

4) 400m

Solution:

In the Electromagnetic method,

Skin depth (d) = 503.8 *√ (ρ/f) -----------------(1)

ρ- resistivity (Ω m)

f – frequency (Hz)

The relation between frequency and depth is

d α ( 1/ √f) ----------------(2)

Therefore depth inversely proportional to the square root of the frequency

So,

d₁* √f₁ = d₂ * √f₂

d₁ = 100 m

f₁= 100 Hz

f₂= 400 Hz

d₂ = (d₁*√f₁) / √f₂

    = (100 * √100) / √400

    = 50 m

Depth (d) = 50 m