An electromagnetic wave is travelling in a lossless, non-magnetic dielectric medium having a dielectric constant _r = 2.25 . The wavelength of the wave in the medium is 4 m and the peak electric field is 60 V/m. If the

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Correct answer: D. B = -3 × 10^ -7 ((π)/(2) y + π × 10^8 t) i T

The speed of the electromagnetic wave in the dielectric medium is

v = \dfrac{c}{\sqrt{\epsilon_r}} = \dfrac{3 \times 10^8}{\sqrt{2.25}} = \dfrac{3 \times 10^8}{1.5} = 2 \times 10^8

m/s.

The amplitude of the magnetic field is

B_0 = \dfrac{E_0}{v} = \dfrac{60}{2 \times 10^8} = 3 \times 10^{-7}

T.

The wave vector is

k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{4} = \dfrac{\pi}{2}

rad/m.

The angular frequency is

\omega = kv = \left(\dfrac{\pi}{2}\right) \times (2 \times 10^8) = \pi \times 10^8

rad/s.

Since the wave propagates in the

-y

direction, the phase argument must be of the form

(ky + \omega t)

.

The direction of propagation is given by the direction of

\vec{E} \times \vec{B}

.
Given

\hat{E} = \hat{k}

and

\hat{v} = -\hat{j}

, we have

\hat{k} \times \hat{B} = -\hat{j}

.
Since

\hat{k} \times \hat{i} = \hat{j}

, it follows that

\hat{B} = -\hat{i}

.

Therefore, the complete vector equation for the magnetic field is:

\vec{B} = -3 \times 10^{-7} \sin\left(\dfrac{\pi}{2} y + \pi \times 10^8 t\right) \hat{i}

T.

Answer:

\vec{B} = -3 \times 10^{-7} \sin\left(\dfrac{\pi}{2} y + \pi \times 10^8 t\right) \hat{i}

T

An electromagnetic wave is travelling in a lossless, non-magnetic...

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