Thread: question about momentum of electric field

Suppose you have 2 parallel opposite charged metal plates, would the energy stored in the electric field have any momentum?

I suppose it does because:

E=mc²

So, when we assume E is the energy in the electric field, i would expect the momentum is:

P = E/c² V

With V being the velocity relative to the observer.

Now the trick question i can't answer and the reason i post this here is: does this E still show inertia when only the field is accelerated? E.g. using a transverse wave on multiple parallel places of increasing or decreasing size next to each other would accelerate the location of E between the plates.

I considered that this would imply violation of conservation of momentum so from that i would expect that this would not show any inertia.
However, it can also be that the momentum is conserved by the current in the wires to the paralel plates.

So, does anyone know something about this?

Do the plates store the energy, or does the gap between the plates store it?

Originally Posted by Jilan

Do the plates store the energy, or does the gap between the plates store it?

For a far a i know it is the E-field that stores the energy in a capacitor (except that in high-Q materials the energy storage is a mix of chemical and E-field energy).
So lets assume a vacuum gap between the plates (or air, that is close enough), than the energy stored in the E-field (the gap!) of a parallel plate capacitor is:

W = e0 V² A / (2d)

The problem with an E-field accelerating by means of a transverse wave (so without acceleration of the source of the e-field), is that you can move the e-field with a velocity higher that c.
When i think about it that way, it is more like moving a shadow, which means acceleration of an e-field by transverse waves would not induce any inertial forces.

Can anybody confirm this?

What exactly do you mean by a transverse wave? A transverse wave of what?

Originally Posted by Jilan

What exactly do you mean by a transverse wave? A transverse wave of what?

One possible configuration would be a series of parallel plates next to eachother:

Code:

phase [pi] 0  .33  .66   1     1.33   1.66      0        .33
U~         -- --- ---- ----- ------ ------- -------- --------- etc
gnd        --------------------------------------------------- etc

Then apply an ac power source to each plate of which the phase is shifted as shown. That would result in a travelling e-field. With the shown configuration it is accelerating as well.
I thought that was called a transverse wave.

edit:
Looking it up in wikipedia shows that it is actually simply called a travelling wave.

If you have oscillating charges won't that create EM waves? Wouldn't photons coming pouring out each end each with momentum hf/c?

Originally Posted by Jilan

If you have oscillating charges won't that create EM waves? Wouldn't photons coming pouring out each end each with momentum hf/c?

Sounds logical, so unless someone has another answer i would think that's it.