Dielectric material in 'induced electric field'

[universal_101]

Hi everyone,

I just wanted to know/understand that, why do the dielectrics don't get polarized, when subjected to induced electric field ?
Because, according to the definition of electric field(which is a vector), it is the force per unit charge, which implies, that electric field has a unique direction at every point in space.

So, if 'induced electric field' also complies with the above definition, then an 'induced electric field' should also polarize a dielectric material, just like a dielectric material is polarized in any charged capacitor !

Thanks

 

[mfb]

I just wanted to know/understand that, why do the dielectrics don't get polarized, when subjected to induced electric field ?

Which induced field do you mean here?
They get polarized from an external field. The polarization changes the internal field which again feeds back to the polarization, but that's a feedback we do not have to care about, we just look at the result and describe that.

 

[universal_101]

Which induced field do you mean here?
They get polarized from an external field. The polarization changes the internal field which again feeds back to the polarization, but that's a feedback we do not have to care about, we just look at the result and describe that.

I'm talking about the usual induced electric filed produced by changing magnetic flux.

I don't follow what are you describing though, please elaborate.

 

[universal_101]

No takers !?

 

[nasu]

How do you know that this field does not polarize the dielectric?

 

[mfb]

I'm talking about the usual induced electric filed produced by changing magnetic flux.

It does not matter where an external electric field comes from.

 

[vanhees71]

It's a bit much for a forum posting. Have a look in a good electrodynamics textbook and check the section about classical (i.e., qualitative) theory of the constitutive relations (classical linear-response theory). The Feynman Lectures vol. II are a good starting point.

 

[universal_101]

How do you know that this field does not polarize the dielectric?

There are different ways to check this, for example a homemade experiment would be to put a short circuited parallel plate capacitor perpendicular to the electric filed, for electric fields produced by charges this capacitor will get charged but for induced electric field there won't be any charging of the capacitor.

All in all induced electric fields don't induce charges in metals or dielectrics, in contrast with the electric field of charges.

It does not matter where an external electric field comes from.

Can you please elaborate, what matters and what doesn't !

I hope you understand my question.

It's a bit much for a forum posting. Have a look in a good electrodynamics textbook and check the section about classical (i.e., qualitative) theory of the constitutive relations (classical linear-response theory). The Feynman Lectures vol. II are a good starting point.

I'll take a look at these references and get back to you !

 

[mfb]

You can edit your posts if you want to add something. I merged the three posts.

Can you please elaborate, what matters and what doesn't !

I hope you understand my question.

Metaquestions about questions don't make it easier to understand what you ask.

All in all induced electric fields don't induce charges in metals or dielectrics

They do.

 

[vanhees71]

What do you mean by "induce charges in metals or dielectrics"? Of course, an external electromagnetic field shifts the charges in the medium, leading to its response to the external field. The total field is then the superposition of the external field and the fields caused by the charge-current distribution caused by the shift of the charges.

If your external field is of very high frequency ($\gamma$-ray range), the creation of an electron-positron pair can happen. Then "induced" even literary means that you create new charges (of course never new net charge due to the strict electric-charge conservation).

 

[universal_101]

They do.

Pure curl electric fields cannot induce charges in any metal, for metals would always tend to have the net electric field zero inside, and any pure curl electric field can be represented to be made of smaller loops or 'curls' using Stoke's theorem. So they always end up having eddy currents inside them, which may be different at different region of the metal depending on it's shape, but there is never any induced charge on the metal surface, for there is no need because of no net electric field in any direction inside the metal.

In other words, induced electric fields due to changing magnetic fields cannot induce any charge in any metal, simply because they are "pure curl" electric fields, which can always be represented, as made up of small loops using Stoke's theorem and therefore no need for any induced for there is no net induced electric field in any direction at the first place.

 

[nasu]

By "induce charge" do you mean something else than "move some charges from one point of the metal to another"?

 

[vanhees71]

Pure curl electric field occur in the time-dependent case, cf. Faraday's Law,
$$\vec{\nabla} \times \vec{E}=-\frac{1}{c} \partial_t \vec{B}.$$
Time dependent fields penetrate inside even good conductors, and thus there is a Lorentz force on the charges in the medium. For metals you have first of all conductivity and an induced current according to Ohm's Law,
$$\vec{j}=\sigma \left (\vec{E} + \frac{\vec{v}}{c} \times \vec{B} \right ).$$

 

[mfb]

for metals would always tend to have the net electric field zero inside

In equilibrium without current flow, or if some symmetry prevents a charge. Actual metals are not perfect, infinite, homogeneous conductors.

 

[Dale]

Pure curl electric fields cannot induce charges in any metal, for metals would always tend to have the net electric field zero inside, and any pure curl electric field can be represented to be made of smaller loops or 'curls' using Stoke's theorem. So they always end up having eddy currents inside them, which may be different at different region of the metal depending on it's shape, but there is never any induced charge on the metal surface, for there is no need because of no net electric field in any direction inside the metal.

In other words, induced electric fields due to changing magnetic fields cannot induce any charge in any metal, simply because they are "pure curl" electric fields, which can always be represented, as made up of small loops using Stoke's theorem and therefore no need for any induced for there is no net induced electric field in any direction at the first place.

Do you have a reference for this? It seems incorrect to me. I think you must be misunderstanding whatever references you got this from.

 

[nasu]

@Universal
How does a receiving antenna work according to your understanding?
But you still did not say what do you mean by "induced charge" in a metal.

 

[universal_101]

By "induce charge" do you mean something else than "move some charges from one point of the metal to another"?

Of course, Inducing charges on the surface of a metal is totally different than inducing current inside the conductor.

 

[universal_101]

Pure curl electric field occur in the time-dependent case, cf. Faraday's Law,
$$\vec{\nabla} \times \vec{E}=-\frac{1}{c} \partial_t \vec{B}.$$
Time dependent fields penetrate inside even good conductors, and thus there is a Lorentz force on the charges in the medium. For metals you have first of all conductivity and an induced current according to Ohm's Law,
$$\vec{j}=\sigma \left (\vec{E} + \frac{\vec{v}}{c} \times \vec{B} \right ).$$

What is the point here ?
whatever you said is fine, though. And should result in induced charges at the surface of the metal due to pure curl electric field.

 

[universal_101]

In equilibrium without current flow, or if some symmetry prevents a charge. Actual metals are not perfect, infinite, homogeneous conductors.

I think it's safe to imagine a static case, where the change in magnetic field is very slow and monotonous, and the metal is also uniform without any symmetry problem.

 

[Dale]

Of course, Inducing charges on the surface of a metal is totally different than inducing current inside the conductor.

Are you familiar with the continuity equation?

What is the point here ?
whatever you said is fine, though. And should result in induced charges at the surface of the metal due to pure curl electric field.

The same is true of a non pure curl electric field.

 

[mfb]

I think it's safe to imagine a static case, where the change in magnetic field is very slow and monotonous, and the metal is also uniform without any symmetry problem.

If you slow down changes in the exterior fields sufficiently then induced charges are negligible, obviously. Where is the point?
See the antenna comment by nasu. Note that antennas are not spread out over all space, so the "infinite" requirement I listed is violated here.

 

[nasu]

Of course, Inducing charges on the surface of a metal is totally different than inducing current inside the conductor.

So where does surface charges come from? They are just created on the spot or they move from other parts of the metal to increase charge density in a specific area?
If they move, what would you call this motion?
Are you saying that induced filed do not move (redistribute) charges on the surface but only in bulk of the metal?
If this is so, how does the skin effect fits in this?

It may be that you have some personal definition of induced charge and maybe even current.
And all this for what? The OP was about induced field not inducing charges in dielectrics. You were asked to provide some reference or evidence that this is so, before asking why is it so. And from there it went to metals and somehow going in circles, re-defining the terms on the way.

 

[universal_101]

Do you have a reference for this? It seems incorrect to me. I think you must be misunderstanding whatever references you got this from.

You can consider any good text on basic electrodynamics to be the reference.

Are you familiar with the continuity equation?

Yes, you mean the charge conservation equation, right?

The same is true of a non pure curl electric field.

So what, the point is being same, they don't behave same.

@Universal
How does a receiving antenna work according to your understanding?
But you still did not say what do you mean by "induced charge" in a metal.

And I thought it would be easy to explain the problem.

I'm supposing that you're talking about a receiving antenna which responds to the incoming electromagnetic waves, therefore, it depends on the shape of the antenna and the orientation of that antenna w.r.t the incoming EM wave.

But you're making a very simple question drastically complicated, I'm saying, that let's suppose we have a solenoid whose current is increasing monotonously, so that magnetic field is also changing monotonously, then accordingly we should get an induced electric field which is pure curl.

Now, we know that this induced electric field is along the lines of vector potential(A), in the form of circular rings around that solenoid, and if we were to put a parallel plate of dielectric or a metal perpendicularly to these circular lines so that the plane of the plate is aligned radially. One must conclude that these plates would get polarized just like they do when we subject them to electric fields produced by charges .

 

[vanhees71]

It's correct that a time-varying magnetic field induces an electric field according to Faraday's, Law,
$$\vec{\nabla} \times \vec{E}+\frac{1}{c} \partial_t \vec{E}=0.$$
The electromagnetic field interacts with the charges within your dielectric or metal. The former gets polarized and in the latter the conduction electrons move. The charges don't get "induced". The charges are there all the time (except if you have hard enough $\gamma$ rays involved that can lead to the creation of electron-positron pairs).

 

[universal_101]

If you slow down changes in the exterior fields sufficiently then induced charges are negligible, obviously. Where is the point?
See the antenna comment by nasu. Note that antennas are not spread out over all space, so the "infinite" requirement I listed is violated here.

Are you trying to say that, it's not possible experimentally, to subject a dielectric or metal to an appreciable "induced electric field" ?

 

[vanhees71]

Of course you can, and they will lead to reactions of the material as any other electric field. I really don't get what you are after here.

Also in the electrostatic case and electric field acts on the charges in an (ideal) conductor. These charges rearrange compared to the configuration without an external eletrostatic field such there's no electric field left inside the conductor when the new static situation is reached. This is called influence and manifests itself in the fact that there accumulates surface charge on the conductor and a charge density within the conductor which exactly compensates the external field inside the conductor.

You can calculate all this analytically for the special case of a spherical conductor, using the method of images.

 

[mfb]

Are you trying to say that, it's not possible experimentally, to subject a dielectric or metal to an appreciable "induced electric field" ?

No. You seem to try to find something that is impossible. Everyone else tells you it is possible, then you add additional constraints, everyone else is telling you it is still possible, and so on.
I get the impression this discussion is quite pointless.

 

[Dale]

You can consider any good text on basic electrodynamics to be the reference.

Please PM me with a specific reference supporting your exact claim here.

Until then thread closed. Please review the forum rules on personal speculation.