If the magnetic field in a plane electromagnetic wav is given by $\overrightarrow{\mathrm{B}}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \mathrm{j} \mathrm{T}$, then what will be expression for electric field?

(C) $\overrightarrow{\mathrm{E}}=\left(9 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}\right)$

(A) $\overrightarrow{\mathrm{E}}=\left(60 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}\right)$

(B) $\overrightarrow{\mathrm{E}}=\left(3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{i}} \mathrm{V} / \mathrm{m}\right)$

(D) $\vec{E}=\left(3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\right)$

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · EM Waves

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If the magnetic field in a plane electromagnetic wav is given by

B = 3 \times 1 0^{- 8} sin (1.6 \times 1 0^{3} x + 48 \times 1 0^{10} t) jT

, then what will be expression for electric field?

(A) $E = (60 sin (1.6 \times 1 0^{3} x + 48 \times 1 0^{10} t) \hat{k} V / m)$
(B) $E = (3 \times 1 0^{- 8} sin (1.6 \times 1 0^{3} x + 48 \times 1 0^{10} t) \hat{i} V / m)$
(C) $E = (9 sin (1.6 \times 1 0^{3} x + 48 \times 1 0^{10} t) \hat{k} V / m)$ ✓ Correct
(D) $E = (3 \times 1 0^{- 8} sin (1.6 \times 1 0^{3} x + 48 \times 1 0^{10} t) \hat{j} V / m)$

Answer: (C)

Solution

In an electromagnetic wave the field amplitudes are tied by

E_{0} = c B_{0}

, so

E_{0} = (3 \times 1 0^{8}) (3 \times 1 0^{- 8}) = 9 V/m

. With

B

along

\hat{j}

and the propagation direction set by the phase,

E

must be perpendicular to both and complete a right-handed set, placing it along

\hat{k}

. Thus

E = 9 sin (1.6 \times 1 0^{3} x + 48 \times 1 0^{10} t) \hat{k} V/m

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 07 Jan 2020 · Shift 1 · EM Waves

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