Q.The energy of an electromagnetic wave is distributed along its electric and magnetic fields in the ratio

Because $E = cB$ in an electromagnetic wave and the energy densities involve $E^2$ and $B^2$ with $c^2 = 1/(\mu_0\varepsilon_0)$, the electric and magnetic energy densities always come out equal.

The energy density (energy per unit volume) stored in the electric field of an EM wave is

$u_E = (1/2)\varepsilon_0 E^2$

and in the magnetic field,

$u_B = \dfrac{B^2}{2\mu_0}$

In an electromagnetic wave, the electric and magnetic field magnitudes are related by $E = cB$, where $c = 1/\sqrt{\mu_0\varepsilon_0}$.

Substitute $B = E/c$ into $u_B$: …