Question

The electric field of a plane electromagnetic wave varies with time of amplitude $2V{m}^{-1}$ propagating along a z-axis. The average energy density of the magnetic field (in $J{m}^{-3}$) is

• A. $13.29\times {10}^{-12}$
• B. $8.86\times {10}^{-12}$
• C. $17.72\times {10}^{-12}$
• D. $4.43\times {10}^{-12}$

Answer 1

Answer: (B)

$8.86\times {10}^{-12}$

Amplitude of electric field and magnetic field are related by the relation
$\frac{E_0}{B_0}=c$

Average energy density of the magnetic field is
$U_B=\frac{1}{4}\frac{B_0^2}{{\mu }_0}=\frac{1}{4}\frac{E_0^2}{{\mu }_0{c}^2}$ $(\therefore B_0=\frac{E_0}{c})$

$\frac{1}{4}{ϵ}_0{E}_0^2$ $(c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}})$

$\frac{1}{4}\times 8.854\times {10}^{-12}\times (2{)}^2=8.854\times {10}^{-12}J{m}^{-3}$

$\approx 8.86\times {10}^{-12}J{m}^{-3}$