The magnetic field in a plane electromagnetic wave is $\mathrm{B}_{\mathrm{y}}=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^{3} \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{T}$. The corresponding electric field will be

(B) $\mathrm{E}_{\mathrm{z}}=105 \sin \left(1.5 \times 10^{3} \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{Vm}^{-1}$

(A) $\mathrm{E}_{\mathrm{y}}=1.17 \sin \left(1.5 \times 10^{3} \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{Vm}^{-1}$

(C) $\mathrm{E}_{\mathrm{z}}=1.17 \sin \left(1.5 \times 10^{3} \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{Vm}^{-1}$

(D) $\mathrm{E}_{\mathrm{y}}=10.5 \sin \left(1.5 \times 10^{3} \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{Vm}^{-1}$

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · EM Waves

The magnetic field in a plane electromagnetic wave is

B_{y} = (3.5 \times 1 0^{- 7}) sin (1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t) T

. The corresponding electric field will be

(A) $E_{y} = 1.17 sin (1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t) Vm^{- 1}$
(B) $E_{z} = 105 sin (1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t) Vm^{- 1}$ ✓ Correct
(C) $E_{z} = 1.17 sin (1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t) Vm^{- 1}$
(D) $E_{y} = 10.5 sin (1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t) Vm^{- 1}$

Answer: (B)

For a plane EM wave,

E_{0} = c B_{0}

. Here

B_{0} = 3.5 \times 1 0^{- 7}

T, so

E_{0} = (3 \times 1 0^{8}) (3.5 \times 1 0^{- 7}) = 105 Vm^{- 1}

The wave argument is

(1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t)

, i.e. it propagates along

- x

. Since

B

is along

\overset{y}{^}

and

\hat{S} = \hat{E} \times \hat{B}

must point along

- \overset{x}{^}

E

must be along

\overset{z}{^}

(as

\overset{z}{^} \times \overset{y}{^} = - \overset{x}{^}

). Hence

E_{z} = 105 sin (1.5 \times 1 0^{3} x + 0.5 \times 1 0^{11} t) Vm^{- 1}

Note: the ratio

ω / k = 0.5 \times 1 0^{11} /1.5 \times 1 0^{3} \approx 3.3 \times 1 0^{7}

m/s does not equal

c

, so the given wave data is internally inconsistent (this was flagged for challenge by the official source); using the standard relation

E_{0} = c B_{0}

as done in the official solution gives option (2).

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Single correct option