# Permitivity of a conductor

1. May 1, 2015

### Prannoy Mehta

It's a dilemma I am in, I am stuck with definitions.
NOTE: I have assumed that all the wires, have no resistance, there is not concept of antilog, etc.

Capacitance in simple words, is the ability of a material to retain charge (and store it).

Force due to charges, when a conductor is placed between them is zero, as the text which I says permittivity, is infinity, hence by columbs law it is zero.

Now, suppose I have a capacitor, I have connected it to a battery (Ideal, no internal resistance, the capacitor, assumed does not breakdown), the plate connected to the positive terminal, has a few till potential becomes equal, moving towards the positive terminal. Now the positive plate induces negative charge on one surface of the other plate, and the other has positive charge, the plate has a higher potential then the negative terminal is it attached to, the electrons from the negative terminal of the battery make the potential zero. That's how a capacitor is charged, roughly speaking, in what I have learned. Using these, and a few others we have derived the basic equation of capacitors. And proved that that capacitance is directly proportional, to the dielectric of the material between them. So for a conductor, filling the space between them entirely, capacitance should be infinity.

Now I do the same charging procedure, with a conductor between them, filling the gap entirely between the two plates of the capacitors, now assuming the plates are conducting.
Due the electric field, applied the conductors free electrons move in the opposite direction of the electric having more negative charge near, the positive plate, and more positive charge near the negative plate. Now if it is conductor. Since one side of the conductor being at lower potential, compared to the other side, since it has a plate in contact with higher potential, excess electrons will flow, and one side becomes neutral, and a similar thing happens with the negative side of the conductor. And it becomes somewhat like a wire connecting both the ends of a battery. Now, according to the definition, given above, there is no charge stored, hence should be zero. But mathematically speaking, we are getting infinity, is there a limitation, of my concept, or is there a limitation, to the concept of dielectric, which I am unable to apply.

And if one does not mind, can just define dielectric in two or three lines, it would be of great help.

All help is appreciated.

NOTE: I got the value of infinity from the text, I am referring to. If we assume it to be zero, the latter problem is solved, but then the force between two charges with a conductor in between them becomes infinity, another dilemma.

2. May 2, 2015

### bsvc

A dielectric is a material that doesn't conduct electricity. There can be current through a dielectric, but only displacement current, (electrons are bound in the material, but are pulled slightly by the electric field, creating dipoles). I think the dielectric constant of most conductors is actually close to vacuum permittivity ε0 (nothing has a dielectric constant of zero, so don't worry about that), or at least a value of 1 is usually used for relative permittivity to calculate the speed of waves in metal. They probably say it is infinite so you can use certain equations where they really shouldn't be applicable. If you replace a capacitor's dielectric with metal, it isn't really a capacitor anymore because the current through it would be drift current, not displacement current, so you couldn't charge it to store energy, as you said. If you have to assign a capacitance value to it anyway, go with infinity, because an infinite ideal capacitor (with no initial voltage) would be electrically the same as a wire (except if you averaged the current through it over infinite time, that would have to be zero). The definition you give for capacitance, "the ability of a material to retain charge," doesn't really describe the quantity, capacitance, that you're calculating very well. A capacitor doesn't store any net charge, it stores energy. (There is something called self-capacitance, which is more like that, but it doesn't matter very often so we don't talk about it) We are interested here in the mutual capacitance between the plates, which is how much charge you have to put onto one plate (and take off the other) to create a certain voltage.

Capacitance is charge squared over energy, so it's sort of the ability of the capacitor to be charged in that higher capacitance means it takes less energy to give it a certain amount of charge.

Last edited: May 2, 2015
3. May 3, 2015

### cnh1995

I
Dielectrics tend to nullify the applied electric field through the dielectric polarization while the conductors cause actual flow of electrons through them opposite to the field (to nullify the field)..Hence we get charge deposition on capacitor plates and current eventually ceases..But if it were a conductor instead, there would be no opposition to applied electric field via polarization,instead a continuous motion of electrons i.e. a current will flow to cancel the field (but it can't cancel it as long as battery is connected and we'll get a non-stop current). Dielectric polarization gives rise to displacement current whose magnitude is same as the instantaneous drift current..

Last edited: May 3, 2015