AQA A2 Physics - Capacitors - Dielectrics?!

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username2638907
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Hi, I'm a bit confused on dielectrics.

Basically I don't really get permittivity. My book says a bigger permittivity means a bigger electric field that opposes the field between the capacitor plates... but why is that?

It says higher permittivity just means it is harder to make a field in the dielectric/material. It doesn't say anything about a bigger field when permittivity is bigger...

Also what does relative permittivity have to do with it? Thanks.
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uberteknik
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(Original post by Barryl)
Hi, I'm a bit confused on dielectrics.

Basically I don't really get permittivity. My book says a bigger permittivity means a bigger electric field that opposes the field between the capacitor plates... but why is that?

It says higher permittivity just means it is harder to make a field in the dielectric/material. It doesn't say anything about a bigger field when permittivity is bigger...

Also what does relative permittivity have to do with it? Thanks.
Permittivity is a property of the dielectric material.

A dielectric material contains insulator atoms such that no current can flow between the plates. In essence, a good dielectric material increases the onset of breakdown voltage. In other words, the capacitor has a much higher working voltage rating.

But it does not stop there. The electrons in the outer shells of the insulating dielectric atoms are however influenced by the electric field between the plates created when the capacitor is charged.

That electric field polarises the dielectric electrons such that they are biased to spend statistically more time attracted to the +ve plate (unlike charges attract) and less time towards the -ve plate (like charges repel).

The effect is rippled through the depth of the dielectric material as adjacent atoms are in very close proximity.

This action is exactly the same as the repulsion between charges on opposite plates and because of the dielectric electron polarisation and close coupled electrons, the overall capacitance is increased. (it has the same effect as reducing the separation between the plates).

The dielectric constant of permittivity is by definition, different for any given material.

It's very unwieldy for engineers and physicists to have ever-changing large tables of dielectric constants hidden away in their back pockets so the concept of relative permittivity was devised.

This simply means that for convenience, the actual permittivity value is split into two components:

\mathcal{E} = \mathcal{E}_0 \mathcal{E}_r

\mathcal{E}_0 is the measured permittivity of free space (vacuum) and does not change. Like all other physical constants it can be memorised.

\mathcal{E}_0 = 8.85 x 10-12 Fm-1

\mathcal{E}_r is simply a scale factor and the figure more easily remembered since it's a low decimal normally stated to 1 decimal place. This is the value capacitor manufacturers will state.

Some common values are:

Vacuum = 1
Teflon/PTFE = 2.1
Polystyrene 2.7
Mylar = 3.1
Tantalum = 27
Niobium = 41

To find the actual permittivity multiply the two.

By inspection, the dielectric plays a vital role in allowing the miniaturisation of capacitors for use in modern electronic devices.
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(Original post by uberteknik)
Permittivity is a property of the dielectric material.

A dielectric material contains insulator atoms such that no current can flow between the plates. In essence, a good dielectric material increases the onset of breakdown voltage. In other words, the capacitor has a much higher working voltage rating.

But it does not stop there. The electrons in the outer shells of the insulating dielectric atoms are however influenced by the electric field between the plates created when the capacitor is charged.

That electric field polarises the dielectric electrons such that they are biased to spend statistically more time attracted to the +ve plate (unlike charges attract) and less time towards the -ve plate (like charges repel).

The effect is rippled through the depth of the dielectric material as adjacent atoms are in very close proximity.

This action is exactly the same as the repulsion between charges on opposite plates and because of the dielectric electron polarisation and close coupled electrons, the overall capacitance is increased. (it has the same effect as reducing the separation between the plates).

The dielectric constant of permittivity is by definition, different for any given material.

It's very unwieldy for engineers and physicists to have ever-changing large tables of dielectric constants hidden away in their back pockets so the concept of relative permittivity was devised.

This simply means that for convenience, the actual permittivity value is split into two components:

\mathcal{E} = \mathcal{E}_0 \mathcal{E}_r

\mathcal{E}_0 is the measured permittivity of free space (vacuum) and does not change. Like all other physical constants it can be memorised.

\mathcal{E}_0 = 8.85 x 10-12 Fm-1

\mathcal{E}_r is the figure more easily remembered since it's a low decimal normally stated to 1 decimal place. This is the value capacitor manufacturers will state.

Some common values are:

Vacuum = 1
Teflon/PTFE = 2.1
Polystyrene 2.7
Mylar = 3.1
Tantalum = 27
Niobium = 41

To find the actual permittivity multiply the two.

By inspection, the dielectric plays a vital role in allowing the miniaturisation of capacitors for use in modern electronic devices.
Sorry... I'm still kind of confused... why does bigger permittivity mean a bigger opposing electric field?
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uberteknik
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(Original post by Barryl)
Sorry... I'm still kind of confused... why does bigger permittivity mean a bigger opposing electric field?

It's because the electric dipole moments of individual dielectric atoms become aligned in opposition to the polarising field across the plates:


Think about that polarising field. The voltage across the plates produces an electric field between the plates in a uniform direction.

The electrons of the dielectric atoms react to that polarising field and will align with opposite charges attracted to the appropriate plates. (Like charges attract, unlike charges repel). Provided that the plate voltage and hence polarising field is not strong enough to cause breakdown of the dielectric: electrons are bound to their parent atoms and as a consequence will still react to the polarising electric field but during each orbit, will spend more time towards the positively charged plate and less towards the negatively charged plate.

i.e. the charged plates will cause dielectric electron orbits to bias themselves away from the negative plate and more towards the positive plate. The collective dielectric dipole moments sum to produce their own electric field which by inspection is in opposition to the polarising electric field across the capacitor plates.

Image

Permittivity is a way of describing the magnitude and ease with which the polarising field aligns the dielectric electrons, including the density of electrons etc. More dielectric electrons in a given volume and the ease with which they react to the polarising field, when aligned, will produce a larger opposing electric field.

In other words, the higher the permittivity, then the greater the opposing electric field produced by the polarising field will be.
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uberteknik
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(Original post by Barryl)
Sorry... I'm still kind of confused... why does bigger permittivity mean a bigger opposing electric field?
Did you read my last explanation and has this now clarified your understanding?
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(Original post by uberteknik)
Did you read my last explanation and has this now clarified your understanding?
I'm still a bit confused:

Permittivity is how hard it is to generate an electric field in a medium, correct?

So why, then, does that mean a bigger "opposing field" is generated when a dielectric with a higher permittivity is used? Surely it would be the same field, but it would just be harder to generate it?

Sorry if I am missing something obvious here...
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uberteknik
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(Original post by Barryl)
I'm still a bit confused:

Permittivity is how hard it is to generate an electric field in a medium, correct?
Yes, correct.


(Original post by Barryl)
So why, then, does that mean a bigger "opposing field" is generated when a dielectric with a higher permittivity is used? Surely it would be the same field, but it would just be harder to generate it?
Think of an analogy, action and reaction. One log of wood cannot hold back the river, but it will still produce a finite resistance to the flow of water. A large obstacle like a beaver dam still made up of logs, sum to produce a resistance to the flow which virtually stops it.


A single dielectric electron placed within the electric field between the capacitor plates, will polarise and produce a finite opposing field which is negligible in comparison to the field created by the charge across the plates. It still has a permittivity albeit an insignificant value. Work was still done to polarise the electron and energy is stored.

Now replace the single electron with trillions of electrons, each and every one producing a miniscule finite opposing field - those individual fields acting in unison, sum to produce a vastly greater opposing field.

The collective permittivity of all those individual dipole fields has therefore increased dramatically. The work done to accomplish this has increased dramatically and so has the stored energy within the electric field between the capacitor plates.
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(Original post by uberteknik)
Yes, correct.




Think of an analogy, action and reaction. One log of wood cannot hold back the river, but it will still produce a finite resistance to the flow of water. A large obstacle like a beaver dam still made up of logs, sum to produce a resistance to the flow which virtually stops it.


A single dielectric electron placed within the electric field between the capacitor plates, will polarise and produce a finite opposing field which is negligible in comparison to the field created by the charge across the plates. It still has a permittivity albeit an insignificant value. Work was still done to polarise the electron and energy is stored.

Now replace the single electron with trillions of electrons, each and every one producing a miniscule finite opposing field - those individual fields acting in unison, sum to produce a vastly greater opposing field.

The collective permittivity of all those individual dipole fields has therefore increased dramatically. The work done to accomplish this has increased dramatically and so has the stored energy within the electric field between the capacitor plates.
Perfect! Thank you!
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