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Ahsan Khan

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- 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 :)

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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