Q. The electric field of a plane electromagnetic wave varies with time of amplitude $2Vm^{- 1}$ propagating along $z$-axis. The average energy density of the magnetic field is (in $Jm^{- 3}$)
A) $13.29 \times 10^{- 12}$
B) $8.86 \times 10^{- 12}$
C) $17.72 \times 10^{- 12}$
D) $4.43 \times 10^{- 12}$
Explanation
(b) 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
$v_{B} = \frac{1}{4}\frac{B_{0}^{2}}{\mu_{0}}$
$= \frac{1}{4}\frac{E_{0}^{2}}{\mu_{0}c^{2}}\ \ \ \ \ \ \left\lbrack \because B_{0} = \frac{E_{0}}{c} \right\rbrack$
$= \frac{1}{4}\varepsilon_{0}E_{0}^{2}\ \ \ \left\lbrack \because c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}} \right\rbrack$
$= \frac{1}{4} \times 8.854 \times 10^{- 12} \times (2)^{2} = 8.854 \times 10^{- 12}Jm^{- 3}$
$= 8.86 \times 10^{- 12}Jm^{- 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.