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

CSIR-NET 2015

99.Compared to an electromagnetic wave of frequency 1.2 MHz travelling in a medium of resistivity 100 ohm-m, the skin depth of a wave of 2.4 MHz travelling in a medium of resistivity 50 ohm-m is

1)decreased by a factor of 2

2)increased by a factor of 2

3)unchanged

4)decreased by a factor of 4

Solution:

In Electromagnetic method,

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

Case (1):

ρ₁- resistivity = 100 Ω m

f₁– frequency = 1.2MHz= 1200000Hz

Form eq (1)

d₁ = 503.8 * (√(100/1200000)) ----------------(2)

d₁= 503.8 * (√(1/12000))

d₁ = 503.8 * 0.00913

d₁ = 4.599 m

Case (2):

ρ₂- resistivity = 50 Ω m

f₂ – frequency = 2.4MHz= 2400000Hz

Form eq (1)

d₂ = 503.8 * (√(50/2400000))

d₂= 503.8 * (√(1/48000))

d₂ = 503.8 * 0.00456

d₂ = 2.299 m

Therefore Case(2) decreases by a factor of 2