An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, sigma=10 mho / m. The ratio of maximum conducting current density to maximum displacement current density is \_\_\_\_。\ [. Take .frac14 pi epsilon_0=9 x 10^9 Nm^2 / C^2]

j_ c=sigma E E => E_0 sin (omega t- kx) j_ c=sigma E_0 sin (omega t- kx) => ( j_ c)_ max =sigma E_0 .......1 J_ d => frac i_ d A=frac1 A x varepsilon_0 frac AdE dt => varepsilon_0 x E_0 omega cos (omega t- kx) ( j_ d)_ max => varepsilon_0 E_0 omega .......2 (i)/(ii) \ frac( j_ c)_ max ( j_ d)_ max =fracsigma E_0varepsilon_0 omega E_0 => fracsigmavarepsilon_0 omega => frac10 x 4 pi x 9 x 10^92 pi x 100 x 10^6 => 1800

An electromagnetic wave of frequency 100 MHz propagates... | null (Physics)

\mathrm{j}_{\mathrm{c}}=\sigma \mathrm{E}\\

\mathrm{E} \Rightarrow \mathrm{E}_{0} \sin (\omega \mathrm{t}-\mathrm{kx})\\

\mathrm{j}_{\mathrm{c}}=\sigma \mathrm{E}_{0} \sin (\omega \mathrm{t}-\mathrm{kx})\\

\Rightarrow\left(\mathrm{j}_{\mathrm{c}}\right)_{\text {max }}=\sigma \mathrm{E}_{0} \tag.......{1}\\

\mathrm{J}_{\mathrm{d}} \Rightarrow \frac{\mathrm{i}_{\mathrm{d}}}{\mathrm{A}}=\frac{1}{\mathrm{~A}} \times \varepsilon_{0} \frac{\mathrm{AdE}}{\mathrm{dt}}\\

\Rightarrow \varepsilon_{0} \times \mathrm{E}_{0} \omega \cos (\omega \mathrm{t}-\mathrm{kx})\\

\left(\mathrm{j}_{\mathrm{d}}\right)_{\text {max }} \Rightarrow \varepsilon_{0} \mathrm{E}_{0} \omega \tag.......{2}\\

(i)/(ii)

\\ \frac{\left(\mathrm{j}_{\mathrm{c}}\right)_{\text {max }}}{\left(\mathrm{j}_{\mathrm{d}}\right)_{\text {max }}}=\frac{\sigma \mathrm{E}_{0}}{\varepsilon_{0} \omega \mathrm{E}_{0}} \Rightarrow \frac{\sigma}{\varepsilon_{0} \omega}\\

\Rightarrow \frac{10 \times 4 \pi \times 9 \times 10^{9}}{2 \pi \times 100 \times 10^{6}}\\

\Rightarrow 1800

Explanation

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