Question #43183

Students often memorize the free-space intensity formula $I = \frac{E_0 B_0}{2\mu_0}$ and assume it universally applies.

In a lossy medium, the complex wave number $k = \beta - i\alpha$ introduces a phase difference $\phi$ between the electric and magnetic fields.

The magnetic field amplitude becomes $B_0 = \frac{\sqrt{\beta^2+\alpha^2}}{\omega}E_0$.

If students blindly use $I = \frac{E_0 B_0}{2\mu_0}$, they calculate an incorrect intensity of $\frac{625}{\pi} \text{ W/m}^2$ (Option B).

The correct physical principle requires evaluating the time average of the cross product $\vec{E} \times \vec{B}$, which naturally accounts for the $\cos\phi$ power factor, effectively filtering out the reactive energy oscillating between the fields and the medium.