Given below are two statements: one is labelled as Assertion (A)...

The average energy density of the electric field is $u_E = \dfrac{1}{4}\epsilon_0 E_0^2$.

The average energy density of the magnetic field is $u_B = \dfrac{B_0^2}{4\mu_0}$.

In vacuum, the speed of light is $c = \dfrac{1}{\sqrt{\mu_0\epsilon_0}}$, and the field amplitudes are related by $E_0 = cB_0$.

Substituting $E_0$ into the expression for $u_E$:
$u_E = \dfrac{1}{4}\epsilon_0 (cB_0)^2 = \dfrac{1}{4}\epsilon_0 \left(\dfrac{1}{\mu_0\epsilon_0}\right) B_0^2 = \dfrac{B_0^2}{4\mu_0} = u_B$.

Thus, the average energy densities are equal, making the Assertion (A) correct. The Reason (R) is also correct and provides the exact mathematical relationship required to prove the Assertion. Therefore, (R) is the correct explanation of (A).

Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)