A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, $\overrightarrow{\mathrm{E}}=6.6 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$. What is $\overrightarrow{\mathrm{B}}$ at this point?

(B) $2.2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

(A) $-2.2 \times 10^{-8} \hat{\mathrm{i}} \mathrm{T}$

(C) $-2.2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

(D) $2.2 \times 10^{-8} \hat{\mathrm{i}} \mathrm{T}$

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · EM Waves

A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time,

E = 6.6 \hat{j} V / m

. What is

B

at this point?

(A) $- 2.2 \times 1 0^{- 8} \hat{i} T$
(B) $2.2 \times 1 0^{- 8} \hat{k} T$ ✓ Correct
(C) $- 2.2 \times 1 0^{- 8} \hat{k} T$
(D) $2.2 \times 1 0^{- 8} \hat{i} T$

Answer: (B)

Solution

For an electromagnetic wave, the magnitudes of electric and magnetic fields are related by

∣ B ∣ = \frac{∣ E ∣}{c}

. Here,

∣ B ∣ = \frac{6.6}{3 \times 1 0 ^{8}} = 2.2 \times 1 0^{- 8}

T. The direction is determined by

\hat{E} \times \hat{B} = \overset{c}{^}

. Since

E = 6.6 \hat{j}

and the wave propagates along

\hat{i}

, we have

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

, giving

B = 2.2 \times 1 0^{- 8} \hat{k}

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Single correct option

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