Answer to Question #153973 in Mechanics | Relativity for Satyam

Question

The Depth of penetration of EM wave in medium having conductivity σ at a frequency of 1 MHz is 25 cm. The depth of penetration at a frequency of 4 MHz will be

Answer 1

Let's write the formula for the depth of penetration at frequency $f_1$:

$$\delta_1=\sqrt{\dfrac{1}{\pi\sigma f_1\mu}},$$

here, $\delta_1=25\ cm$ is the depth of penetration at frequency $f_1=10^6\ Hz$, $\sigma$ is the conductivity of the material, $\mu$ is the permeability.

Similarly, we can write the formula for the depth of penetration at frequency $f_2 = 4\cdot10^6\ Hz$:

$$\delta_2=\sqrt{\dfrac{1}{\pi\sigma f_2\mu}}.$$

Let's divide $\delta_1$by $\delta_2$, we have:

$$\dfrac{\delta_1}{\delta_2}=\sqrt{\dfrac{f_2}{f_1}}.$$

From this formula, we can find $\delta_2$:

$$\delta_2=\delta_1\sqrt{\dfrac{f_1}{f_2}}=25\ cm\cdot\sqrt{\dfrac{10^6\ Hz}{4\cdot10^6\ Hz}}=12.5\ cm.$$

Answer:

$\delta_2=12.5\ cm.$