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

Gate_2020

3) Skin depths in homogeneous media of resistivity $\rho_{1}$ and $\rho_{2}$ are 100 m and 200 m respectively at 1000Hz frequency. The ration of $\rho_{1}$/$\rho_{2}$ will be _________

(Thanks to Chandrasekhar, ANU)

Solution:

Skin depth $\delta_{1}$ at $\rho_{1}$ and f is given  100 m

Skin depth $\delta_{2}$ at $\rho_{2}$ and f is given  200 m

Formula 

 

$\delta =503.8\sqrt{\frac{\rho}{f}}$

$\frac{\delta_{1}}{\delta_{1}}=\frac{503.8\sqrt{\frac{\rho_{1}}{f}}}{503.8\sqrt{\frac{\rho_{2}}{f}}}$

$\frac{100}{200}=\sqrt{\frac{\rho_{1}}{\rho_{1}}}$

$(0.5)=\sqrt{\frac{\rho_{1}}{\rho_{1}}}$

${\frac{\rho_{1}}{\rho_{1}}}= 0.25$