Electric field in a plane electromagnetic wave is given by $$E=50 \sin \left(500 x-10 \times 10^{10} t\right) \mathrm{V} / \mathrm{m}$$ The velocity of electromagnetic wave in this medium is : (Given C = speed of light in vacuum)

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · EM Waves

Electric field in a plane electromagnetic wave is given by

E = 50 sin (500 x - 10 \times 1 0^{10} t) V / m

The velocity of electromagnetic wave in this medium is :
(Given C = speed of light in vacuum)

(A)C
(B) $\frac{C}{2}$
(C) $\frac{2}{3} C$ ✓ Correct
(D) $\frac{3}{2} C$

Answer: (C)

Solution

Comparing

E = 50 sin (500 x - 10 \times 1 0^{10} t)

with

E_{0} sin (k x - ω t)

gives

k = 500 m^{- 1}

and

ω = 10 \times 1 0^{10} rad s^{- 1}

. The wave speed is

v = \frac{ω}{k} = \frac{10 \times 1 0 ^{10}}{500} = 2 \times 1 0^{8} m s^{- 1} .

Since

C = 3 \times 1 0^{8} m s^{- 1}

, this equals

v = \frac{2}{3} C

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Single correct option

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