The electric field and magnetic field components of an… — JEE Main 2023 Physics PYQ

JEE Main 2023 · 24 Jan · Shift 2

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by

E_x = E_0 \sin(kz - \omega t)

B_y = B_0 \sin(kz - \omega t)

Then the correct relation between

E_0

and

B_0

is given by

A.
$E_0 = kB_0$
B.
$E_0 B_0 = \omega k$
C.
$\omega E_0 = kB_0$
D.
$kE_0 = \omega B_0$

Show answer and solution

Correct option: D

Solution

From Maxwell's equations, the relation between E and B in an EM wave comes from Faraday's law: ∂E_x/∂z = -∂B_y/∂t. Differentiating: kE₀cos(kz-ωt) = ωB₀cos(kz-ωt), giving kE₀ = ωB₀. This is consistent with the fact that E₀/B₀ = ω/k = c (speed of light in vacuum).

[JEE Main 2023 · 24 Jan · Shift 2]

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