JEE Physics 2023 Question with Solution

Given: The question asks for the energy density expressions associated with the electric field $E$ and magnetic field $B$ of an electromagnetic wave in free space.

Find: The correct expressions for $U_E$ and $U_B$.

By theory of electromagnetic waves:

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

and

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

Thus, the electric field energy density is proportional to $\epsilon_0 E^2$ and the magnetic field energy density is proportional to $\frac{B^2}{\mu_0}$.

Therefore, the correct option is A.

Given: An electromagnetic wave in free space.

Find: Which option matches the standard energy density formulas.

Quick Tip: For electromagnetic waves, the energy is shared equally between the electric and magnetic fields. The standard expressions are:

$$U_E = \frac{1}{2}\epsilon_0 E^2, \qquad U_B = \frac{B^2}{2\mu_0}$$

Matching these directly with the options gives A.

Therefore, the correct option is A.