A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) $\overrightarrow{\mathrm{E}}=9.6 \hat{\mathrm{j}} \mathrm{V}/\mathrm{m}$. The value of magnetic field at this point is:

(A) $3.2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

(B) $3.2 \times 10^{-8} \hat{\mathrm{i}} \mathrm{T}$

(C) $9.6 \hat{\mathrm{j}} \mathrm{T}$

(D) $9.6 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · EM Waves

A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time)

E = 9.6 \hat{j} V / m

. The value of magnetic field at this point is:

Answer: (A)

For a plane electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by

E = c B

B = \frac{E}{c} = \frac{9.6}{3 \times 1 0 ^{8}} = 3.2 \times 1 0^{- 8} T

The direction of

B

follows from the propagation direction

\overset{v}{^} = \hat{i}

and the field direction

\hat{E} = \hat{j}

, using

\hat{B} = \overset{v}{^} \times \hat{E} = \hat{i} \times \hat{j} = \hat{k}

B = 3.2 \times 1 0^{- 8} \hat{k} T

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Single correct option