The energy density associated with electric field \vecE and magnetic field \vecB of an electromagnetic wave in free space is given by (\epsilon_0-. permittivity of free space, \mu_0- permeability of free space)

U_E=\frac\epsilon_0 E^22, U_B=\fracB^22 \mu_0

U_E=\fracE^22 \epsilon_0, U_B=\frac\mu_0 B^22

U_E=\frac\epsilon_0 E^22, U_B=\frac\mu_0 B^22

U_E=\fracE^22 \epsilon_0, U_B=\fracB^22 \mu_0

Electromagnetic Waves PYQ — JEE Main 2023 · 6 Apr · Shift 2 · Q48 with Solution

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Correct answer: A

For an electromagnetic wave in free space, the standard expressions for energy density are:

$U_E = \frac{1}{2}\epsilon_0 E^2$

and

$U_B = \frac{1}{2\mu_0} B^2$

Option A: $U_E = \frac{\epsilon_0 E^2}{2}, \quad U_B = \frac{B^2}{2\mu_0}$ This matches the standard formulas exactly.
Option B: $U_E = \frac{E^2}{2\epsilon_0}, \quad U_B = \frac{\mu_0 B^2}{2}$ Both expressions are incorrect.
Option C: $U_E = \frac{\epsilon_0 E^2}{2}, \quad U_B = \frac{\mu_0 B^2}{2}$ Electric part is correct, magnetic part is incorrect.
Option D: $U_E = \frac{E^2}{2\epsilon_0}, \quad U_B = \frac{B^2}{2\mu_0}$ Magnetic part is correct, electric part is incorrect.

$\boxed{A}$