Question

Consider an electromagnetic wave propagating through a region of empty space. How is the energy density of the wave partitioned between the electric and magnetic fields?

Answer 1

Answer:

$u=\frac{1}{2}(\epsilon_oE^2+\frac{1}{\mu_o}B^2)$

Explanation:

To assemble a distribution of charges, the work or energy required against the Coulomb repulsion of like charges is given by :

$W_e=\frac{\epsilon_o}{2} \int E^2d\tau$

where, $E$ is the resulting electric field due to the distribution of charges.

Similarly, the work required to get currents going against the back emf,

$W_m=\frac{1}{2\mu_o} \int B^2d\tau$

where, $B$ is the resulting magnetic field.

The integrations are volume integrals. Hence, the total energy stored in the electromagnetic fields, per unit volume is given by

$u=\frac{1}{2}(\epsilon_oE^2+\frac{1}{\mu_o}B^2)$