An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, _r=9 , has the electric field, E_x=E_0 (kz-2π×10^6 t) Vm ^ -1 where E_0 is the amplitude and k is the wave vector. Among

Question

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Correct answer: C. The wavelength of the electromagnetic wave inside the medium is 300 m

From the given equation of the electric field

E_x = E_0 \sin(kz - 2\pi \times 10^6 t)

, the wave is propagating in the

+z

direction.

The angular frequency is

\omega = 2\pi \times 10^6

rad/s, which gives the frequency

f = \dfrac{\omega}{2\pi} = 10^6

Hz.

The speed of the electromagnetic wave in the dielectric medium is given by

v = \dfrac{c}{\sqrt{\mu_r \epsilon_r}}

.

Assuming a non-magnetic medium (

\mu_r = 1

), we get

v = \dfrac{3 \times 10^8}{\sqrt{9}} = 10^8

ms

^{-1}

.

The wavelength of the wave inside the medium is

\lambda = \dfrac{v}{f} = \dfrac{10^8}{10^6} = 100

m.

Option (3) states the wavelength is

300

m, which is incorrect.

An electromagnetic wave travelling in a lossless dielectric medium...

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