GATE EC 2010 Electromagnetics Solution Q 2

GATE EC 2010 Electromagnetics Solution Q 2

The electric field component of a time harmonic plane EM wave travelling in in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time average power density vector (in W/m2) is

(a) \frac1{30\pi}

(b) \frac1{60\pi}

(c) \frac1{120\pi}

(d) \frac1{240\pi}

Ans : c)

Explanation

Magnitude of the time-average power density vector or Poynting vector is given as,

P_{av}=\frac{E^2}{2\eta} \eta=\sqrt{\mu/\in}=\sqrt{\frac{\mu_0}{\varepsilon_0\varepsilon_r}}=\frac{120\pi}{\sqrt4} P_{av}=\frac{1^2}{2\left({\displaystyle\frac{120\pi}2}\right)}=\frac1{120\pi}W/m^2

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