Lets say we have vacuum capacitor.
which is made of 2 plates and vacuum between them.
lets say we somehow charge it and leave

now according to e=mc^2 capacitor mass consists of mass of plates + mass of stored energy.

but where that energy mass is held? in the void between plates(vaccum somehow gains mass) or plates become more heavy?

the dieletric of a capacitor is there as a way to control the speed of the discharge between the plates. The dielectric does not store any charge, but the discharge between the plates will pass through it.

I guess to answer your question, One plate would become heavier until discharge.

A flying saucer acts a capacitator it stores energy (area51)

if there is dielectric we can expect it to store energy in the polarization effect

I am not talking about mass of electrons, but about mass of energy itself

Um, does a spring that has been compressed get heavier?

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Uhum , I think you have the same kind of question about potential energy as I have in the OP : E=mc² where I ask about the effect of potential energy .
My answer to your remark , till now , is , yes the spring should have more energy (and therefor mor mass ) after compression.

Without doubt answer is yes.

e=mc^2 does refer to total energy, including potential energy (which is relative to a ground state and hard to make absolute--but then mass isn't absolute either--but I'd guess you'd need to measure with respect to an ultimate ground state--say, the entire universe in a singularity). So, the plates (both, I'm sure--positive charges and negative charges both being forms of potential energy) would get unmeasurably heavier.

Not counting, of course, the small added weight to one plate from getting some extra electrons and the equivalent small subtracted weight from the other plate, which would probably be a bigger effect than the relativistic one.

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Hmm, maybe I understood everythin wrong in my physics lesson. E=mc^2 does not mean Energy has mass. It means Enrgy and mass are equivalent. It is wheter energy or mass and can be converted into each other under some circumstances.

For example annihilation of matter/antimatter, before you have mass, after you have energy.
Same for the so called mass defect in nuclei. The particles (protons & Neutrons) have bigger mass when seperated. When togehter bound some of the mass is lost and goes into binding energy.

So to my opinion the capacitor does not gain any mass. But I may be completely wrong.

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Andre

"They did not know it was impossible, so they did it!"
Mark Twain

Maxwell would have said the energy is in the 'displacement current'. The way he decided to deal with electromagnetism is similar to this situation.

I feel the energy would be stored on the plates themselves as static charges. We could easily just say the energy is stored in the electic field between the plates though.

imagine black box where you have positron and electron they definitely have rest mass, and now they annihilate and increase temperature inside the box or we can use that energy to charge capacitor.

so does it mean that box weights less mow?
probably not, so that means that capacitor charge also has same mass like every other material energy form. which is also equally attracted by gravity

I would say the box weigh less now. The mass has been converted into energy. And after stored into the capacitor it is still energy, not mass.

As said before, I maybe understood relativity wrong. Even though I have a degree in physics, I have never been good in theoretical physics.

ETA: MAybe Publius shows up to sort this out.

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Andre

"They did not know it was impossible, so they did it!"
Mark Twain

that is obviously wrong, because we could use this to create perpetual motion engine:

imagine that you have matter + antimatter they have weight and pull the lever down, now you annihilate them and store energy in the capacitor, weight becomes less so lever goes up. then you convert capacitor energy back into matter+ antimatter, cycle repeats and it can even produce usable work.

If you have a box with a positron and an electron in it, and they annihilate, then you have a box with two .511 MeV photons in it. Technically, it dosent have a temperature, it isnt in equilibrium.

The mass of the box (assuming the photons are still bound in the box) is unchanged.

At no time could you use the contents of the box to charge a capacitor, since there was never any net charge present to charge the capacitor.

To answer the OP: If you charged a cap, yes the mass would go up a very very very tiny amount, that amount would be dependent on the energy needed to charge the capacitor. To first order, the energy is in the electric field across the plates of the capacitor. Exactly speaking, the energy is bound into the potential between every two like charges forced into the cap.

this is similar to the slight increase in mass due to the binding energy of a molecule

Not sure if I understand your example completely, but for sure there would be unavoidable losses during the conversion of the enrgy into electricity to store it in the capacitor.

But anyway, as I said before I have really some doubts about my understanding of relativity. So I better should bow out and listen to what others have to say.

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Andre

"They did not know it was impossible, so they did it!"
Mark Twain

bold mine: I think Digix meant to use the energy of the annihilation an transfer it by some means of "dynamo" into electric energy.
But as said in my previous post: I better stay out of this discussion.

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Andre

"They did not know it was impossible, so they did it!"
Mark Twain

theoretically it is possible to perform lossless process so that is not important


ok, but i don't think that it is necessary
also I have very bad experience trying to find at least someone who would think in relativistic mass change way instead of space time dilution.

there was one discussion what if some piece falls into black hole and hits singularity with extreme kinetic energy.

Just to complete the thought, where I was going was this:

I thought a capacitor stored energy as the different densities of electrons in the two plates.

...so I was wondering about the mass related effects on the electrons themselves.

But then I realised any effect on the -ve plate would be "balanced" by the +ve plate.

So that went nowhere.

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Measure once. Cut twice. Power tools are fun.

I would say the E=mc² equation doesn't apply here for the total energy in a physical sense for the following reason :
Suppose you have an uncharged capacitor , enclose it by a box and call its mass m . So you have an internal energy of E=mc².
Now you charge it by applying a delta V over the poles . What happens is that some electrons move from one plate to another . The number of electrons missing on one plate will be found on the other plate , so delta m will be zero , meaning there is no delta energy contributed to mass.
What happens is that an electric field is created by the opposite charges.
The energy of this field is Efield=1/2*Q²/C , where C is the capacitance :
C= eta*A/d , so Efield = 1/2Q²*d/(eta*A). One can write this in terms of the voltage also .
The Energy simply comes from charges with are stored at different potential level , not from an increase of mass , und thus has an electrical ground .
Best way to represent the energy from my point of view is :
Etot = mc² + Efield.
Of course one can write the equivalent mass to be : meq= Etot/c² , but this lacks a bit of physical sense .
Writing this way means information is lost about where the energy really comes from : electrostatic energy .
I think in standard calculations where electromagnetic fields are involved , such as Eel, Bmagn the mass , charge are always kept apart and are not mixed in a relativistic way : Finertia = d(mv)/dt ; Fel=qE; Fmagn=q(vxB)+ Maxwell equations