Question

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

Here, $E_0=2V{m}^{-1},B_0=E_0/c$
and $c=\frac{1}{\sqrt{{\mu }_0{\in }_0}}$
Average energy density of magnetic field is
$U_B=\frac{1}{2}\frac{B_0^2}{{\mu }_0}=\frac{1}{4}\frac{E_0^2}{{\mu }_0{c}^2}$
$=\frac{1}{4}{ϵ}_0{E}_0^2$
$=\frac{1}{4}\times \left(8.85\times 10^{-12}\right)\times 2^2$
$=8.854\times 10^{-12}J{m}^{-3}$
$=8.86\times 10^{-12}J{m}^{-3}$