During the propagation of electromagnetic wave in a particular medium:

We begin by recalling the expressions for energy densities associated with electric and magnetic fields in any linear, homogeneous medium.

For the electric field, the energy density is given by the formula

$$u_E=\frac12\,\epsilon\,E^2,$$

where $$\epsilon$$ is the permittivity of the medium and $$E$$ is the instantaneous electric-field magnitude.

For the magnetic field, the corresponding formula is

$$u_B=\frac12\,\frac{B^2}{\mu},$$

where $$\mu$$ is the permeability of the medium and $$B$$ is the instantaneous magnetic-field magnitude.

Now, an electromagnetic wave is a self-sustaining combination of mutually perpendicular electric and magnetic fields that travel together with speed

$$v=\frac1{\sqrt{\mu\,\epsilon}}.$$

Maxwell’s equations further give the relation between the amplitudes of the fields in a plane wave:

$$\frac{E}{B}=v.$$

Substituting $$v=\dfrac1{\sqrt{\mu\,\epsilon}}$$ into this relation, we get

$$E = \frac{B}{\sqrt{\mu\,\epsilon}}.$$

We now compare the two energy densities. First we write the electric energy density explicitly in terms of $$B$$ by substituting the above expression for $$E$$:

$$u_E = \frac12\,\epsilon\,\left(\frac{B}{\sqrt{\mu\,\epsilon}}\right)^2.$$

Simplifying step by step, we have

$$u_E = \frac12\,\epsilon\,\frac{B^2}{\mu\,\epsilon} = \frac12\,\frac{B^2}{\mu}.$$

But $$\dfrac12\,\dfrac{B^2}{\mu}$$ is exactly the formula we already wrote for $$u_B.$$ Therefore,

$$u_E = u_B.$$

This equality holds for every point and at every instant within the electromagnetic wave as it propagates through the medium. Consequently, the electric energy density is neither greater nor smaller than the magnetic energy density; they are identical.

Hence, the correct answer is Option C.