# B Dielectric material in 'induced electric field'

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1. Sep 28, 2015

### 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

2. Sep 28, 2015

### Staff: Mentor

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.

3. Sep 28, 2015

### universal_101

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

4. Sep 29, 2015

### universal_101

No takers !!?

5. Sep 29, 2015

### nasu

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

6. Sep 29, 2015

### Staff: Mentor

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

7. Sep 30, 2015

### 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.

8. Oct 1, 2015

### universal_101

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.

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

I hope you understand my question.

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

Last edited by a moderator: Oct 2, 2015
9. Oct 2, 2015

### Staff: Mentor

You can edit your posts if you want to add something. I merged the three posts.
Metaquestions about questions don't make it easier to understand what you ask.
They do.

10. Oct 3, 2015

### 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).

11. Oct 5, 2015

### universal_101

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.

12. Oct 5, 2015

### nasu

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

13. Oct 5, 2015

### 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,
$$\vec{j}=\sigma \left (\vec{E} + \frac{\vec{v}}{c} \times \vec{B} \right ).$$

14. Oct 5, 2015

### Staff: Mentor

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

15. Oct 5, 2015

### Staff: Mentor

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

Last edited: Oct 6, 2015
16. Oct 5, 2015

### 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.

17. Oct 8, 2015

### universal_101

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

18. Oct 8, 2015

### universal_101

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.

Last edited: Oct 8, 2015
19. Oct 8, 2015

### universal_101

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.

20. Oct 8, 2015

### Staff: Mentor

Are you familiar with the continuity equation?

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