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

CSIR-NET 2014

93. A conducting ore body buried under a conducting medium of 10 ohm-m could not be located by electromagnetic methods utilizing a frequency of 1000Hz, but could be located utilizing a frequency of 250Hz. The ore body lies between

1) 0-25 m 

2) 25-50 m 

3) 50-100 m 

4) 100-200 m

Solution:

In the Electromagnetic method,

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

(i) Conducting medium of 10 Ωm could not be located by EM methods utilizing a frequency of 1000 Hz

ρ₁- resistivity = 10 Ω m

f₁– frequency = 1000 Hz

Form eq (1)

d₁ = 503.8 * (√(10/1000))

d₁= 503.8 * (√(1/100))

d₁ = 50.38 m

(ii) Conducting medium of 10Ω m could be located by EM method utilizing a frequency of 250 Hz

ρ₂- resistivity = 10 Ω m

f₂ – frequency = 250 Hz

Form eq (1)

d₂ = 503.8 * (√(10/250))

d₂= 503.8 * (√(1/25))

d₂ = 503.8 / 5

d₂ = 100.76 m

Therefore Ore body lies between the 50 – 100 m depth