# Momentum in electromagnetic waves

• I
• Ahsan Khan
In summary, the conversation discusses the topic of EM waves and the concepts of momentum and energy in relation to them. The conversation covers the basic level understanding of EM waves and their energy and momentum, as well as Einstein's energy-momentum relation. The conversation also mentions a physics book and a photograph for further understanding of the topic. The speaker expresses a desire to understand the physics behind the equations and concepts discussed.
Ahsan Khan
TL;DR Summary
I need to know how my book "University Physics" arrived at one of it's equation on momentum density dp/dV= S/c^2.
Hi all!
These days I am brushing up my knowledge on EM Waves. I begin with the introductory level but I don't mind to engage in an advanced treatment of the topic.

At the very basic level I had a high school book, the mentions straightway that if the wave carries with it an energy U, it posses a momentum p= U/c (8.12), where c is the speed of light.

I also heard about what they call Einstein's energy momentum relation. The total energy E by a wave/particle (with rest mass m0 if it's a particle) having momentum p by the following relation.
E^2 = (pc)^2 + (m0c^2) ^2

For a wave(EM wave) m0=0, so E= pc and this gives p=E/c.
This is kind of proof of my basic text if I believe in the famous Einstein Energy-momentum relation just mention above.
One of the problems I feel is that I don't know the Physics behind Einstein Energy-mometum relation so it's like memorising the stuff rather than understanding the reality of nature. So the proof is not complete in this sense.

Another thing is that I come across; is on a page in the book University Physics by Sears and Zemansky 12th Edition, where they talk about Electromagnetic momentum flow and radiation pressure.

They say it can be shown the electromagnetic wave carry momentum p, with a corresponding momentum density (momentum dp per volume dV) of magnitude

dp/dV= EB/μοc^2 = S/c^2 (32.30)
(I know EB/μο= Poynting Vector magnitude and other symbols).

I am attaching the photograph of both the books.
I need particularly the physics (proof) behind momentum density equation 32.30 of University Physics book and if possible the insight into Einstein Energy momentum relation also.

Regards!
Thanks a bunch :)

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Last edited:
bhobba

## 1. What is momentum in electromagnetic waves?

Momentum in electromagnetic waves refers to the energy and motion carried by the wave as it propagates through space. It is a measure of the wave's ability to transfer energy and cause a change in momentum in the particles it interacts with.

## 2. How is momentum related to the frequency and wavelength of an electromagnetic wave?

The momentum of an electromagnetic wave is directly proportional to its frequency and inversely proportional to its wavelength. This means that as the frequency of the wave increases, its momentum also increases, while a decrease in wavelength leads to an increase in momentum.

## 3. Can momentum be transferred from an electromagnetic wave to an object?

Yes, momentum can be transferred from an electromagnetic wave to an object through the process of radiation pressure. When the wave interacts with the object, it exerts a force on it, causing a change in momentum. This phenomenon is used in technologies such as solar sails.

## 4. How does the momentum of an electromagnetic wave differ from that of a particle?

The momentum of an electromagnetic wave is different from that of a particle because it is dependent on the wave's energy and frequency, rather than its mass and velocity. Additionally, electromagnetic waves can have both linear and angular momentum, while particles only have linear momentum.

## 5. What is the significance of momentum in electromagnetic waves?

Momentum is an important concept in understanding the behavior and interactions of electromagnetic waves. It helps explain phenomena such as the reflection, refraction, and diffraction of waves, as well as their ability to transfer energy and cause changes in momentum in matter. Additionally, the concept of momentum is essential in the development and application of technologies that utilize electromagnetic waves, such as wireless communication and medical imaging.

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