# Magnetic fields and energy in a capacitor

## Main Question or Discussion Point

In a capacitor, specifically a parallel plate capacitor, ideally we have that capacitance is a function of permittivity, separation, and plate area. Does permeability play any role? Is all the energy stored in the electric field? Please consider this in a charge static state and also when (dis)charging (thus there is current).

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jim hardy
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i was unable to find a constant that relates permeability to permittivity
so i think that in your static state, there's no current hence no H field so permeability isn't a factor

even though a real dielectric probably has permeability somewhat different than free space .

and i believe one might at first say the energy is all stored in the dielectric ,
perhaps to begin forming his mental picture one could even think of it as as mechanical work done in rotating the polar molecules out of their rest position and into alignment with the field... like winding a clockspring.

From there, like all things one can refine it ad infinitum
so it becomes for a practical capacitor , "nearly allstored in dielectric"
surely there's a minute amount of energy on the plate itself due to densification or rareification of charge on it

a search on "relationship permeability permittivity" took me to many scholarly articles.
The one by R F Harrington of ntu.edu.tw looked not overly abstruse.

just old jim , not much of a scholar

Well this looks like a homework question to me.

Jim, I agree with your static analysis.

In the dynamic case how fast can a change be propagated from one plate to the other.

Hint : What is 1/√(εμ) ?

jim hardy
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Thanks Studiot

your hint says in just 17 ascii characters(including spaces) what would have taken me pages. That is genius, my friend!

old jim

P.S. .....thanks for the constant......

In a capacitor, specifically a parallel plate capacitor, ideally we have that capacitance is a function of permittivity, separation, and plate area.
So far, so good.

Does permeability play any role?
No.

Is all the energy stored in the electric field?
Yes.

Please consider this in a charge static state and also when (dis)charging (thus there is current).
A capacitor has the same net charge of ZERO, whether there is no voltage or any voltage you can name between its plates. However many coulombs of charge are put on one plate, an equal number of coulombs are removed from the other plate. This causes a voltage to form between the plates and an electrostatic field to form, which stores electrical energy. A capacitor is not "charged" or "discharged". It is instead "energized" and "de-energized". A moving current sustains a magnetic field, but it is not an energy storage mechanism in a capacitor.

jim hardy,

even though a real dielectric probably has permeability somewhat different than free space .
You mean permittivity, not permeability. All materials including vacuum have a permittivity value, so what is a "real" dielectric?

and i believe one might at first say the energy is all stored in the dielectric
It is stored mostly in the space occupied by the dielectric, except for the fringe electric field. Whenever a electric field exists, energy is involved.

Ratch