1. Energy densities in an electromagnetic wave

For an electromagnetic wave propagating in a medium, the instantaneous energy densities are:

$u_E = \frac{1}{2}\,\varepsilon E^2$

and

$u_B = \frac{B^2}{2\mu}$

where $\varepsilon$ is the permittivity and $\mu$ is the permeability of the medium.

2. Relation between $E$ and $B$ in a medium

For an electromagnetic wave in a medium,

$v = \frac{1}{\sqrt{\mu\varepsilon}}$

and also

$E = vB$

So,

$E^2 = v^2 B^2 = \frac{1}{\mu\varepsilon} B^2$

3. Substitute into electric energy density

$u_E = \frac{1}{2}\varepsilon E^2 = \frac{1}{2}\varepsilon \left(\frac{1}{\mu\varepsilon}B^2\right) = \frac{B^2}{2\mu}$

But

$u_B = \frac{B^2}{2\mu}$

Hence,

$u_E = u_B$

4. Evaluate options

• A: Electric energy density is double of magnetic energy density. ❌
• B: Electric energy density is half of magnetic energy density. ❌
• C: Electric energy density is equal to magnetic energy density. ✅
• D: Both are zero. ❌

5. Final answer

The correct option is:

$\boxed{\text{C}}$