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

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

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

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

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




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