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
$\delta
=503.8\sqrt{\frac{\rho}{f}}$
$\frac{\delta_{1}}{\delta_{1}}=\frac{503.8\sqrt{\frac{\rho_{1}}{f}}}{503.8\sqrt{\frac{\rho_{2}}{f}}}$
$\frac{100}{200}=\sqrt{\frac{\rho_{1}}{\rho_{1}}}$
$(0.5)=\sqrt{\frac{\rho_{1}}{\rho_{1}}}$
${\frac{\rho_{1}}{\rho_{1}}}=
0.25$
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