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

CSIR-NET 2014 DEC

105) If an electric field of strength 100mV/km is injected in the ground and the strength of the recorded magnetic field is 1500gamma, the corresponding apparent resistivity at time period 1000s,is

A) 0.9Ωm  
B) 15Ωm 
C) 100Ωm 
D) 5Ωm

Solution:

 $ Apparent resistivity, \rho_a=0.2T\mid\frac {E_x}{H_y}\mid^2 Ωm ------(1)$

$Electric field(E_x)=100 mV/km$

$Magnetic field (H_y) = 1500 gammas (or) nT(nano tesla)$

Time period(T)=1000s

Substitute in eq(1)

$\rho_a = 0.2\times 1000 \times \mid\frac{100}{1500}\mid^2$

$= 0.2\times 1000 \times \frac{100 \times 100}{1500 \times 1500}$

  $= \frac{8}{9}=0.88 Ωm$

$\rho_a=0.9 Ωm$