The energy of an electromagnetic field is related to both its amplitude and frequency. The energy carried by an electromagnetic wave is proportional to the square of its electric field amplitude.
The energy density (u) of an electromagnetic wave is given by the equation:
u = (ε₀/2) * E²
where ε₀ is the permittivity of free space and E is the electric field amplitude. As you can see, the energy density is directly proportional to the square of the electric field amplitude.
The frequency of an electromagnetic wave determines the energy of individual photons or quanta of energy associated with the wave. According to Planck's equation, the energy of a single photon (E) is given by:
E = h * f
where h is Planck's constant and f is the frequency of the electromagnetic wave. This equation shows that the energy of a photon is directly proportional to its frequency.
So, the energy of an electromagnetic field is determined by the amplitude of the electric field (for a given frequency) and the frequency of the wave. Both factors play a crucial role in determining the total energy carried by the electromagnetic field.