Understanding Dielectric Constants and Their Impact on Capacitance

[learning_phys]

The higher the dielectric constant, the higher the capacitance right?

I am reading that water has a dielectric constant of 80. This means the capacitance is 80 times greater (if there was water between the parallel plate capacitor) than if the capacitor was in vacuum.

What is the dielectric constant of a conductor? Say copper? Since it allows current flow, would it have a negative dielectric constant?

If so, then a dielectric constant = -inf would be a perfect conductor? dielectric constant of inf would be a perfect insulator?

 

[learning_phys]

also, can anyone explain the D field? D and E are related by E=permittivity*E which means that if there's a dielectric with high permititivity, then you would have a very large D field. What does it mean physically to have a D field near infinity?

For high-k dielectrics, what exactly does an increased D-field mean (what physically increases? and why is it greater than E?)

 

[learning_phys]

really confused, any thoughts??

 

[will.c]

There is no such thing as the dielectric constant of a conductor. A dielectric is, by definition, nonconducting. Electric displacement "D" is also not just epsilon * E, it also includes a polarisation term.

 

[learning_phys]

what is a dielectric with dielectric costant = inf?

 

[learning_phys]

does it mean the material perfectly cancels the electric field between the plates?

 

[vishal_garg]

no you are wrong.
vacuum is perfect insulator which has dielectric constant=1

 

[merryjman]

Dielectric constants can be larger than one. The dielectric constant is a simple linear approximation factor which compares insulators. When electric fields penetrate matter, the atoms inside the matter will polarize and partially cancel out the field inside the matter.

I suppose theoretically that a perfect insulator would have an infinite dielectric constant, since it would be able to completely cancel any penetrating E-field. In real life, however, once the E-field becomes strong enough, it will polarize the atoms inside so strongly that they will be ripped apart (ionized) and then current will flow. Have you ever gotten a static shock? In that case, the charges on your fingers created such a strong E-field that the air molecules were ionized and therefore conducted electricity. This is called "dielectric breakdown" and is a bad thing for electronic devices :)

The D-field is what's left over of the E-field after it has been partially canceled by polarization. A D-field, then, can't be infinite; it can only be slightly less strong than the electric field which created it.

 

[learning_phys]

what is you have a high dielectric constant? Then D=k*epsilon*E which means for very large k, we will get D=inf right? How is it possible for the d-field to be LESS than the E field for large dielectric constant?

 

[merryjman]

I was wrong to say that the D field is less than the E field. The two don't have the same units, so I can't really compare them that way. What I should have said is that the D field is a vector sum of the E-field(times $$\epsilon_{0}$$) and the P-field (polarization of the insulating material):$$\vec{D} = \epsilon_{0} \vec{E} + \vec{P}$$

When a dielectric is placed in an external field, the atoms polarize, and the P-field points in the opposite direction of the E-field. So looking at the expression above, the sum is less than (e0)E. In a conductor, the E field is completely canceled by the rearrangement of charges, and in a dielectric the cancellation is not total.

It can also be confusing that there are several epsilon terms out there. If you use the "permittivity" rather than "vacuum permittivity" the above expression can be simplified to

$$\vec{D} = \epsilon \vec{E}$$

 

[learning_phys]

so what does it mean to have a displacement field to be infinity?

Since D is proportional to k, then what does it mean to have a dielectric with a high permittivity (what does it mean to have D->inf)

 

[merryjman]

In the case of a capacitor, a large permittivity means that it can "store" more charge with a smaller electric field. So it can hold more energy. But all real materials have a limit to how large an electric field they can handle before getting ionized. So neither the k value nor the D field could be infinite, because this would imply a material could handle an infinitely large electric field.

 

[Gear300]

The overall result of putting a conductor is nothing...it does not provide for a new dielectric constant (this in respect to ideal conductors)

 

[learning_phys]

In the case of a capacitor, a large permittivity means that it can "store" more charge with a smaller electric field. So it can hold more energy. But all real materials have a limit to how large an electric field they can handle before getting ionized. So neither the k value nor the D field could be infinite, because this would imply a material could handle an infinitely large electric field.

I understand that this is not practical. I just want a sense of what it means to have a very large D-field in a theoretical sense. There are dielectric constants in a the tens of thousands, so in a purely hypothetical sense, what happens when the dielectric constant goes to infinity? what does this physically do? and what does it mean for the D-field to approach infinity?

 

[merryjman]

I think that a nearly infinite dielectric constant would imply that (again in the case of a dielectric placed in an external E field) no matter how strong the applied electric field was, the material would be able to polarize enough to prevent ionization. So I guess this would imply nearly infinite energy storage. I don't understand D intuitively enough to know if it could be very large.

 

[learning_phys]

I think that a nearly infinite dielectric constant would imply that (again in the case of a dielectric placed in an external E field) no matter how strong the applied electric field was, the material would be able to polarize enough to prevent ionization. So I guess this would imply nearly infinite energy storage. I don't understand D intuitively enough to know if it could be very large.

thus a perfect insulator?

 

[dlgoff]

What is the dielectric constant of a conductor?

A dielectric is a nonconducting substance...

http://en.wikipedia.org/wiki/Dielectric"

Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium, and is determined by the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material.

http://en.wikipedia.org/wiki/Permittivity

 

[Herminso]

How effective a dielectric is at allowing a capacitor to store more charge depends on the material the dielectric is made from. Every material has a dielectric constant k. This is the ratio of the field without the dielectric (Eo) to the net field (E) with the dielectric:
k = Eo/E
E is always less than or equal to Eo, so the dielectric constant is greater than or equal to 1. The larger the dielectric constant, the more charge can be stored.

If a metal was used for the dielectric instead of an insulator the field inside the metal would be zero, corresponding to an infinite dielectric constant. The dielectric usually fills the entire space between the capacitor plates, however, and if a metal did that it would short out the capacitor - that's why insulators are used instead.

 

[teachmemore]

How effective a dielectric is at allowing a capacitor to store more charge depends on the material the dielectric is made from. Every material has a dielectric constant k. This is the ratio of the field without the dielectric (Eo) to the net field (E) with the dielectric:
k = Eo/E
E is always less than or equal to Eo, so the dielectric constant is greater than or equal to 1. The larger the dielectric constant, the more charge can be stored.

If a metal was used for the dielectric instead of an insulator the field inside the metal would be zero, corresponding to an infinite dielectric constant. The dielectric usually fills the entire space between the capacitor plates, however, and if a metal did that it would short out the capacitor - that's why insulators are used instead.

So what if said conductor was coated with a high-breakdown, insulative material? Could this composite then be used as a dielectric which would have high permittivity? ie. it insulates, yet it also cancels out the field between the plates perfectly.

 

[teachmemore]

So what if said conductor was coated with a high-breakdown, insulative material? Could this composite then be used as a dielectric which would have high permittivity? ie. it insulates, yet it also cancels out the field between the plates perfectly.

I think I have the answer (please correct me if I'm wrong).

The answer would be 'yes', such a dielectric would have perfect permittivity.

If such a dielectric were used in a capacitor, you would gain the advantage of having perfect permittivity allowing the charge to build up on the plates until it reaches the voltage potential of the charging circuit. - but the energy density of such a capacitor would be limited by the breakdown strength of the dielectric and by of course the surface area of the electrodes; the breakdown strength being significantly reduced by having a conductive layer in it. So what you gain in permittivity, you lose in breakdown strength of the dielectric.

 

[teachmemore]

I think I have the answer (please correct me if I'm wrong).

The answer would be 'yes', such a dielectric would have perfect permittivity.

If such a dielectric were used in a capacitor, you would gain the advantage of having perfect permittivity allowing the charge to build up on the plates until it reaches the voltage potential of the charging circuit. - but the energy density of such a capacitor would be limited by the breakdown strength of the dielectric and by of course the surface area of the electrodes; the breakdown strength being significantly reduced by having a conductive layer in it. So what you gain in permittivity, you lose in breakdown strength of the dielectric.

I just realized that this is totally impractical because the conductive plate in the dielectric would keep the voltage across the electrodes at 0V. Which means that once you got the charge on the plates, it would never leave - you would have to somehow gain access to that middle plate to ever get your charge back.