A plane electromagnetic wave of frequency 100 MHz is traveling in vacuum along the x -direction. At a particular point in space and time, $\overrightarrow{\mathrm{B}}=2.0 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$. (where, $\hat{\mathrm{k}}$ is unit vector along z -direction) What is $\vec{E}$ at this point? (speed of light $c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ )

(B) $6.0 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$

(A) $0.6 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$

(C) $0.6 \mathrm{k} \mathrm{V} / \mathrm{m}$

(D) $6.0 \mathrm{k} \mathrm{V} / \mathrm{m}$

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · EM Waves

A plane electromagnetic wave of frequency 100 MHz is traveling in vacuum along the x -direction. At a particular point in space and time,

B = 2.0 \times 1 0^{- 8} \hat{k} T

. (where,

\hat{k}

is unit vector along z -direction) What is

E

at this point? (speed of light

c = 3 \times 1 0^{8} m / s

)

(A) $0.6 \hat{j} V / m$
(B) $6.0 \hat{j} V / m$ ✓ Correct
(C) $0.6 kV / m$
(D) $6.0 kV / m$

Answer: (B)

Solution

In a plane electromagnetic wave in vacuum the field magnitudes are related by

E = c B

E = 3 \times 1 0^{8} \times 2.0 \times 1 0^{- 8} = 6.0 V/m

The vector

E \times B

points along the direction of propagation. The wave travels along

\hat{i}

and

B

lies along

\hat{k}

, and

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

, so

E

lies along

\hat{j}

. Hence

E = 6.0 \hat{j}

V/m.

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option

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