Question

The electric field of a plane electromagnetic wave of amplitude $2 Vm^{-1}$ varies with time and propagates along z-axis. The average energy density of the magnetic field ($in \,Jm^{-3}$) 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, $E_{0}=2 V m^{-1}, B_{0}=E_{0} / c$
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} \epsilon_{0} E_{0}^{2} $
$=\frac{1}{4} \times\left(8.85 \times 10^{-12}\right) \times 2^{2} $
$=8.854 \times 10^{-12} J m^{-3}$
$=8.86 \times 10^{-12} J m^{-3}$