A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive $x$-direction. At a particular point in space and time, $\overrightarrow{\mathrm{E}}=6.3 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$. The corresponding magnetic field $\overrightarrow{\mathrm{B}}$, at that point will be

(B) $2.1 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

(A) $18.9 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

(C) $6.3 \times 10^{-8} \hat{\mathrm{kT}}$

(D) $18.9 \times 10^{8} \hat{\mathrm{k}} \mathrm{T}$

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · EM Waves

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive

x

-direction. At a particular point in space and time,

E = 6.3 \hat{j} V / m

. The corresponding magnetic field

B

, at that point will be

(A) $18.9 \times 1 0^{- 8} \hat{k} T$
(B) $2.1 \times 1 0^{- 8} \hat{k} T$ ✓ Correct
(C) $6.3 \times 1 0^{- 8} \hat{kT}$
(D) $18.9 \times 1 0^{8} \hat{k} T$

Answer: (B)

Solution

In an electromagnetic wave the field magnitudes are tied by

\frac{E}{B} = c

, so

B = \frac{E}{c} = \frac{6.3}{3 \times 1 0 ^{8}} = 2.1 \times 1 0^{- 8}

T. The direction follows from

\hat{k} \times E

pointing along

B

: with the wave travelling along

+ x

and

E

along

+ \hat{j}

, the magnetic field must point along

+ \hat{k}

, so

B = 2.1 \times 1 0^{- 8} \hat{k}

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

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