22. Skin Depth in homogeneous media of resistivity \rho_{1} and \rho_{2} are 100 m and 200 m respectively, at 1000Hz frequency. The ratio \frac{\rho_{1}}{\rho_{2}} will be __________.
(Thanks to Pragnath, AU)
Solution:
Skin depth formula D = 503.8 * \sqrt{(\frac{\rho}{f})}
Given that,
D_{1}= 100m~,D_{2}= 200 m; f=1000~Hz
\frac{D_{1} = 503.8 * \sqrt{(\frac{\rho_{1}}{f})}}{D_{2} = 503.8 * \sqrt{(\frac{\rho_{2}}{f})}}
\frac{100}{200}=\frac{503.8
* \sqrt{(\frac{\rho_{1}}{1000})}}{ 503.8 * \sqrt{(\frac{\rho_{2}}{1000})}}
\frac{1}{2}=\frac{\sqrt{(\frac{\rho_{1}}{1000})}}{\sqrt{(\frac{\rho_{2}}{1000})}}
\frac{1}{2}=\frac{\sqrt{(\rho_{1}}}{\sqrt{(\rho_{2}})}
Squaring on both sides we
get
\frac{1}{4}=\frac{{\rho_{1}}}{\rho_{2}}
\frac{{\rho_{1}}}{\rho_{2}}=0.25
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