NCERT Solutions for Chapter: Electromagnetic Waves, Exercise 4: LA

An infinitely long thin wire carrying a uniform linear static charge density $\lambda$ is placed along the $z$-axis. The wire is set into motion along its length with a uniform velocity $v=u{\hat{k}}_z$. Calculate the pointing vector $\mathrm{S}=\frac{1}{{\mathrm{\mu }}_{\mathrm{o}}}\left(\mathrm{E}\times \mathrm{B}\right)$.

Sea water at frequency $\nu =4\times {10}^8 \mathrm{Hz}$ has permittivity $\epsilon \approx 80 {\epsilon }_o$, permeability $\mu \approx {\mu }_{\mathrm{o}}$ and resistivity $\mathrm{\rho }=0.25 \Omega –\mathrm{m}$. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source $V\left(t\right) = V_o \sin \left(2\pi \nu t\right)$. What fraction of the conduction current density is the displacement current density?

A plane EM wave travelling along $z$ direction is described by $E=E_0\sin (kz-\omega t)\hat{i}$ and $B=B_0\sin (kz-\omega t)\hat{j}$. Show that

The average energy density of the wave is given by

$U_{aV}=\frac{1}{4}{\epsilon }_0{E}_0^2+\frac{1}{4}\frac{B_0^2}{{\mu }_0}$

A plane EM wave travelling along $z$ direction is described by $E=E_0\sin (kz-\omega t)\hat{i}$ and $B=B_0\sin (kz-\omega t)\hat{j}$. Show that

The time averaged intensity of the wave is given by 

$I_{aV}=\frac{1}{2}C{\epsilon }_0{E}_0^2$