Understanding the Momentum of Changing Electric Fields

[WaveObserver]

Is it fair to say that any changing electric field (hence electrodynamic) has momentum?

 

[dacruick]

I don't think so.

 

[G01]

No it isn't. A changing E-field alone does not carry momentum. You have to consider with it the induced B-field and the Poynting vector.

The momentum density stored in the electromagnetic field is given by:

$$\rho_{EM}=\mu_0\epsilon_0 \vec{S}=\mu_0\epsilon_0 (\vec{E}\times \vec{B})$$

There's a few pieces of information we can gain from this equation:

1. Momentum can only be stored in a field that has non zero E and B.

2. The fields do not need to be time varying. Even a static field can have momentum, as long as its Poynting vector is not zero.

 

[WaveObserver]

Thank you very much GO1.

So in the example I had the Poynting vector would be non zero. But that is not the case for all electric fields and all conditions. If either E or B are zero then you have no momentum.

GO1 do you use a tool for creating latex equations or are you just entering the codes?

 

[G01]

Your welcome!

Physics Forums, being the great place that it is, has Latex built in:

https://www.physicsforums.com/showthread.php?t=386951

You can also click on the $\Sigma$ box on the reply to page to pull up a handy latex code library.