Question

The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magniude of the time average power density vector $\left(inW/m^2\right)$ is

• A. $\frac{1}{120\pi }$
• B. $\frac{1}{30\pi }$
• C. $\frac{1}{240\pi }$
• D. $\frac{1}{60\pi }$

Answer 1

The correct option is A $\frac{1}{120\pi }$

Ans : (c)

Magnitude of the time-average power density vector,

$P_{av}=\frac{E^2}{2\eta }$

where, $\eta =\sqrt{\mu /ϵ}$

$\eta =\sqrt{\frac{{\mu }_0}{4{ϵ}_0}}=\frac{{\eta }_0}{2}=\frac{120\pi }{2}$

$P_{av}=\frac{1^2}{2\left(\frac{120\pi }{2}\right)}=\frac{1}{120\pi }W/m^2$