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  1. Consider a charged particle (electron or proton) at rest. It is surrounded by its own electric field.

  2. Now consider an electron moving with certain velocity (less than speed of light), Still is there electric field around it?

    i. If it has electric field around it, why is it that when electrons are moving in a conductor (i.e.. current if flowing in a conductor) there is no electric field outside the conductor?

    ii. Now, when a current is flowing in a conductor (I'm not sure what happens if the motion is not inside conductor) it produces magnetic field around it. I'm lost. What happened to the electric field? Is it still there? Are there both electric field & magnetic field? Why don't we discuss about it?

  3. Hypothetically, If the electron is moving with speed more than that of light. What happens now?

I'm totally lost. Kindly some one clarify these issues.

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Part 3 is out of the scope of this site, but otherwise it's not a bad question. –  David Z Oct 18 '11 at 20:18
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3 Answers

2.Now consider an electron moving with certain velocity (less than speed of light), Still is there electric field around it?

There is still an electric field associated with the moving charge, but there is now also a magnetic field. Only moving charges can experience this magnetic force.

i. If it has electric field around it, why is it that when electrons are moving in a conductor (i.e.. current if flowing in a conductor) there is no electric field outside the conductor?

For an ideal conductor of zero resistance and carrying a finite current, the electric force on the conduction electrons approaches zero. Therefore the electric field is zero inside. This is achieved by a static rearrangement of the electrons inside to create a static electric field that cancels any other internal electric fields.

However, there is still an external electric field from the excess charge in the wire that comes from the current source. Think of a capacitor slowly discharging where there is an electric field in the region between the plates, but no electric field inside the plates carrying the current.

ii. Now, when a current is flowing in a conductor (I'm not sure what happens if the motion is not inside conductor) it produces magnetic field around it. I'm lost. What happened to the electric field? Is it still there? Are there both electric field & magnetic field? Why don't we discuss about it?

A moving charge has a magnetic and electric field, which can be derived from the Lienard-Wiechert potentials This is all discussed in any book on electricity and magnetism at the undergraduate level.

3.Hypothetically, If the electron is moving with speed more than that of light. What happens now?

Special relativity teaches us that there is a universal speed limit that the speed of light happens to travel at and electrons therefore cannot travel faster than the speed of light, no matter how much energy you put in.

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I believe your response to (i) is not quite correct. This argument would apply to the field inside an ideal conductor, but the electrons inside the conductor don't care about the field outside because the field outside does not affect their equilibrium. –  Jonathan Gleason Oct 19 '11 at 1:34
    
@JonathanGleason I interpreted the question asking why isn't there an electric field outside the conductor from the electric fields of the moving electrons inside. If the arrangement of the charge inside the conductor makes the electric field zero everywhere inside, then it follows they contribute a zero electric field everywhere outside, which shouldn't need explaining, because it seems obvious. –  John McVirgo Oct 19 '11 at 21:59
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"If the arrangement of the charge inside the conductor makes the electric field zero everywhere inside, then it follows they contribute a zero electric field everywhere outside . . ." I don't think this is true. Consider an infinite cylindrical shell with nonzero surface charge density $\sigma$. By symmetry and Gauss's Law, the electric field is zero inside, but nonzero outside. –  Jonathan Gleason Oct 20 '11 at 21:53
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@JonathanGleason yes you're right so +1 for your comment. –  John McVirgo Oct 21 '11 at 13:00
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i. If it has electric field around it, why is it that when electrons are moving in a conductor (i.e.. current if flowing in a conductor) there is no electric field outside the conductor?

This is not the case in general. A conducting material that has reached a steady state will have zero electric field inside the conductor, but the field outside the conductor is determined by the net charge on the conductor as well as its shape. That being said, it is definitely possible to have a setup with flowing electrons and no electric field. If you have a loop of wire with a number of unmoving positive charges that matches the number of moving electrons, there will be no electric field outside the wire, because the net charge is zero.

To be more specific, the electric field produced by an electron is superimposed on the electric field produced by a proton, and the resultant field is effectively zero when you are far enough away compared to the separation distance of the two charges.

ii. Now, when a current is flowing in a conductor (I'm not sure what happens if the motion is not inside conductor) it produces magnetic field around it. I'm lost. What happened to the electric field? Is it still there? Are there both electric field & magnetic field? Why don't we discuss about it?

Again, if there is a net charge, there will be a net electric field. If there is not, then there will be no electric field. There will also be a magnetic field as a result of the charges moving.

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What do you mean by the conducting material that has reached the steady state by? –  AaKASH Mar 26 '13 at 6:02
    
@Adam Strandberg. I think there need not be zero electric field around a neutral (no net charge) body. If we consider a neutral body, containing one electron and one proton, the net charge will be zero, but the electric field will be zero if and only if the distance between proton and electron is zero. If I am wrong here. Please, correct me. –  Godparticle Dec 24 '13 at 20:43
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Still is there electric field around it?

Yes. The electron is moving (in our reference frame), so now there is a magnetic field (in our reference frame), but nothing happens to the electric field.

i. If it has electric field around it, why is it that when electrons are moving in a conductor (i.e.. current if flowing in a conductor) there is no electric field outside the conductor?

The electrons in the conductor produce an electric field outside the conductor; however, realistically, there will be just as many protons in the conductor as electrons, and hence the net electric field outside the conductor is zero.

ii. Now, when a current is flowing in a conductor (I'm not sure what happens if the motion is not inside conductor) it produces magnetic field around it. I'm lost. What happened to the electric field? Is it still there? Are there both electric field & magnetic field? Why don't we discuss about it?

The electric field is still there (in some sense), but its zero, because the electrons and protons in the conductor cancel each other out, so we don't care about it. (Actually, I believe that if you take into account relatavistic effects, which is probably silly not to do in the context of electrodynamics, there will be a nonzero electric field). That being said, if for some reason there were stream of moving electrons with no protons, then we would observe both a (nonzero) magnetic and electric field.

  1. Hypothetically, If the electron is moving with speed more than that of light. What happens now?

Special relativity says this can't happen :). In any case, if we play dumb for a moment, the only thing that would change is the current, and hence the strength of the magnetic field.

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" there is a magnetic field (in our reference frame)" wait a minute! If we are in a frame which is moving with same speed as that of electron. Then there is no magnetic field? How is this possible? I mean, how can magnetic field depend on frame of reference? Its a field. right? –  claws Oct 19 '11 at 6:05
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@claws This is a great question. You are hitting upon something that eventually led to the idea that there is no electric field, nor is there the magnetic field, but only the electromagnetic field. That is to say, whether you observe an electric field, a magnetic field, or a "mixture" of the two is dependent on your frame of reference, i.e., the electric and magnetic fields are really just two sides of the same coin. Regardless of whether you see the electric field or the magnetic doing the job, i.e. regardles of your frame of reference, you will still observe the same physical results. –  Jonathan Gleason Oct 19 '11 at 20:39
    
Wow! It totally sounds weird & abstract. Can you suggest a good book to read further on this topic? –  claws Oct 20 '11 at 16:42
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@claws I believe that the discussion in Grffith's Electrodynamics text that begins on pg. 522 should be what you're looking for. –  Jonathan Gleason Oct 20 '11 at 22:11
    
Your answer says that the external electric field is zero, which is wrong as you pointed out to me. The wires will carry an excess/deficient electron charge, generally. Think of a capacitor carrying a current with differing electron charge on each plate. –  John McVirgo Oct 21 '11 at 13:19
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