# Energy of an electromagnetic wave

• rmberwin
In summary, there is a contradiction between the wave model and the quantum model regarding the energy of an EM wave. According to the wave model, the energy is proportional to the energy in the E and B fields, while according to the quantum model, the energy is proportional to the frequency of the photons. However, when considering a system with a large number of photons, the average number of photons per unit volume can be related to the classical electric and magnetic fields, and their energy per unit volume. Therefore, the energy of an EM wave can be understood as the sum of the energy of each photon.

#### rmberwin

I'm trying to teach myself some basic physics, and so maybe this question is stupid! But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon is simply proportional to the frequency of the light. There seems to be a contradiction here. What am I missing?

The basic answer is that Quantum Mechanics is ultimately correct. An EM wave is made up of many photons, each of which has a discrete, quantized energy value, so the energy of an EM wave is the sum of the energy of every photon.

But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon is simply proportional to the frequency of the light. There seems to be a contradiction here. What am I missing?

Could you please state more carefully where do you see the contradiction? The two sentences talk about different things; the wave and the photon.

For a system with a very large number of photons (any macroscopically measurable electromagnetic field), you can relate the average number of photons per unit volume to the strength of the classical electric and magnetic fields via the energy per unit volume.

although, there doesn't need to be any energy per unit volume. There could just be a plane wave which is transporting energy, which has zero energy per volume.

But yeah, I think that is the rough idea. The energy of a classical EM wave is given by both the frequency of the wave and the amplitude of the electric and magnetic fields. So, we can relate the frequency of the wave to the frequency of each of the photons, and the amplitude of the fields to the number of photons per volume.

edit: wait, no sorry, that's totally incorrect. there does need to be energy per unit volume, which is proportional to E2+B2

## 1. What is the energy of an electromagnetic wave?

The energy of an electromagnetic wave is the amount of energy carried by the wave as it travels through space. It is a form of energy that is constantly present in the universe and can manifest in various forms such as light, radio waves, and X-rays.

## 2. How is the energy of an electromagnetic wave calculated?

The energy of an electromagnetic wave is calculated using the equation E=hf, where E is the energy, h is Planck's constant, and f is the frequency of the wave. This equation is known as the Planck-Einstein relation and is used to determine the energy of individual photons within the electromagnetic wave.

## 3. What factors affect the energy of an electromagnetic wave?

The energy of an electromagnetic wave is affected by two main factors: the frequency of the wave and the amplitude of the wave. As frequency increases, so does the energy of the wave. Similarly, as the amplitude increases, the energy of the wave also increases.

## 4. How does the energy of an electromagnetic wave relate to its wavelength?

The energy of an electromagnetic wave is inversely proportional to its wavelength. This means that as the wavelength increases, the energy of the wave decreases. This relationship is known as the inverse relationship and is described by the equation E=hc/λ, where c is the speed of light and λ is the wavelength.

## 5. What are the practical applications of understanding the energy of electromagnetic waves?

Understanding the energy of electromagnetic waves is crucial in many fields, including telecommunications, astronomy, and medical imaging. It allows us to harness these waves for various purposes such as communication, imaging, and energy production. It also helps us understand the behavior of light and other forms of electromagnetic radiation, which is essential in many scientific and technological advancements.