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I know that a time varying magnetic field produces an electric field even in the absence of a conducting body, because thats how em waves work. But can you say the same for a space varying magnetic field i.e. would there be an electric field if you move a magnet simply in space in the absence of a conducting body?

Here I am trying to understand the difference between electric field generated due to relative motion between a conductor and a magnetic field, and the electric field generated due to a time varying magnetic field.

I feel they are different because in case of relative motion between the conductor and the magnetic field the electrons experience Lorentz magnetic force, leading to the accumulation of electrons at one end of the conductor and hence producing an electric field. So here I see that a space varying magnetic field requires a conducting body to produce electric field; but I don't think a time varying field requires any conducting body to produce electric field. Somebody help!!!!!

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  • $\begingroup$ How would the conducting body know whether the varying magnetic field it experiences is caused by a time varying magnetic field of one sorts (no moving magnet) or another (with moving magnet)? $\endgroup$ – CuriousOne May 10 '15 at 13:14
  • $\begingroup$ Have you looked at Maxwell's equations before? $\endgroup$ – Kyle Kanos May 10 '15 at 13:48
  • $\begingroup$ YEah i also thought that, the magnetic field associated with the conducter will change in both cases but i think thats what farrday is also trying to say..i.e changing flux is what causing both these emf....but induced emf is represented as ((E+vB).dl)..I think in case of emf due to relative motion the (vB) part is causing the emf and in case of time varying magnetic field the (E) part is causing the emf which is the electric field generated by time varying magnetic field..but in case of motional emf electric field is only due to accumalation of e by lawrence manetic force But i am not sure $\endgroup$ – Siddharth Prakash May 10 '15 at 15:11
  • $\begingroup$ sorry it is (vxB) not (vB)..and No i have not yet started on maxwell's equation..I am still stuck on nduction $\endgroup$ – Siddharth Prakash May 10 '15 at 15:13
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    $\begingroup$ If I may suggest one general rule with physics that might help to untangle your problem: always assume that "all physics is local", i.e. that the observer of a phenomenon doesn't know anything about the source of a phenomenon and that a source doesn't care about the type of the observer. So far this rule hasn't failed in physics. In your case that means the electric potential difference induced in a conducting loop is independent of how the time varying flux trough it was created. I don't know if Mr. Faraday understood it this way or not, but that would be irrelevant to nature, anyway. $\endgroup$ – CuriousOne May 10 '15 at 20:53
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First, let's look at terminology (which is important when you've learnt a particular phrasing of the laws). A time-varying magnetic field is when a magnetic field at a point is changing in time. A space-varying magnetic field is when the magnetic field is varying in space. And that means a static magnet is sufficient to produce a space-varying magnetic field; a moving magnet produces a time-varying magnetic field (and yes, it's space-varying too).

Now obviously, the moving magnet produces a circulating electric field around it: if you draw any loop in space, and the magnet goes through it, the flux through the loop changes in time, producing an emf and so forth, according to Faraday's law.

So, to answer your question, if you move a magnet simply in space, there is an electric field that goes around it, following it as it goes. It's almost like the magnetic field if you send a short localized "pulse" of positive, immediately followed by negative, current moving through a wire (which you can't though - without a complicated charge removal mechanism - and we're ignoring other induction effects).

Perhaps you meant to ask what happens when the magnet is stationary, and the conducting rod goes through the field. We'll look at it from the rest frame of the magnet. At first, there is no electric field - it is the magnetic Lorentz force itself (which emphatically does not require a space-varying magnetic field) that is causing the emf in the rod, and moving the charges to the ends. There is equilibrium when the electric field created due to this polarization of the rod creates an equal and opposite emf. But you've said this much already.

The interesting question to ask here is: what is causing the polarization in the rest frame of the conducting rod, where $v = 0$ and there is no magnetic Lorentz force? The answer is that the magnet is moving in this frame, producing a time-varying magnetic field. And that means the electric field is back, and this polarizes the rod, until the charges compensate with an opposing electric field.

In summary, an electric field, when not caused by charges, is caused only by a time varying magnetic field (a space varying magnetic field is a magnetostatic field, and produces no electric field of its own). And the presence of an electric field might depend on your frame of reference (something that is explained better by special relativity).

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  • $\begingroup$ Producing an emf it has to be spend energy like in an antenna. A permanent magnet, moving in free space has to slow down to convert his kinetic energy into emf or does not slow down, hence does not radiate (in the sense of an antenna). See my second answer. $\endgroup$ – HolgerFiedler May 12 '15 at 3:42
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    $\begingroup$ @HolgerFiedler Why would you think a uniformly moving magnet radiates? There is a non-vanishing Poynting vector, but it's just what is necessary for the fields to follow the magnet. A uniformly moving magnet is already generating the emf - it does not have to lose its kinetic energy, just as a stationary point charge which generates an emf between two different concentric spheres does not have to lose energy (of any kind). $\endgroup$ – AV23 May 12 '15 at 13:33
  • $\begingroup$ sorry I think i used terms without understanding there complete meaning...I was under the wrong impression that a moving magnet doesnot produce a time varying field..I thought it produced a space varying field since the magnet was moving in space.. $\endgroup$ – Siddharth Prakash May 12 '15 at 17:51
  • $\begingroup$ I was trying to understand the differnce between the emf generated when you move a conducter in a stationary magnetic field and the emf generated when you move a magnetic field around a sationary conducter.Correct me if i am wrong but i think the origin of force is different in both cases. In the first case I think magnetic lorentz force is causing electrons to move and in second case it is the electric force generated by the induce electric field.I believe this is what you explained in the last two paragraph I hope Mr HolgerFiedler would agree on this. $\endgroup$ – Siddharth Prakash May 12 '15 at 17:58
  • $\begingroup$ Yes, you are right. (Ignore the rest of this comment if you don't care at present for relativity) But the difference is much more subtle in special relativity - the two situations are in fact equivalent, and the emf comes from the same effect. It is just that in different frames of reference, you see different electric and magnetic fields causing the same thing. $\endgroup$ – AV23 May 12 '15 at 18:04
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Now obviously, the moving magnet produces a circulating electric field around it: if you draw any loop in space, and the magnet goes through it, the flux through the loop changes in time, producing an emf and so forth, according to Faraday's law.

This is the second answer I give here and the short answer is again No. A moving magnet doesn't produce in the absence of charges any electric field.

This is evident due to the fact, that a magnet in free space (without friction and air resistance) moves like every body on his inert way and does not go slower and slower. This, braking, happens only in case if there is a body nearby, in which of course will be induced a electric field.

I think @av23 is wrong with his statement, from which follows clear that a moving magnet in free space get stopped after some time. Producing emf the magnet has to lose energy and this could be only kinetic energy. A moving magnet isn't an antenna rod. He does not radiate in the sense of an antenna.

Again, placing any body for measurement near the magnet you get an electric field. And the magnet feels a braking force. But this was not the OPs question. He asked about the electric field in the absence of any body.

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  • $\begingroup$ A moving magnet does produce an electric field. There is braking when this electric field transfers energy to, say electrons, in another material. $\endgroup$ – AV23 May 12 '15 at 13:35
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But can you say the same for a space varying magnetic field i.e would there be an electric field if you move a magnet simply in space in the absence of a conducting body?

Clear answer, no. In the absence of a second body, containing electrons, protons or neutrons a permanent magnet does not induce a electric field. But this is right or not depending from the point of view. The QED representatives works with permanent fields and disturbances in it.

Old school man deal with electrons magnetic dipole moment and related intrinsic spin. If close to the permanent magnet moves a body (containing above mentioned elementary particles) the permanent magnet induces the alignment of the magnetic dipole moments, this aligned the spins too and due to gyroscopic effect the charges start to move inside a metallic body. This is the electric current you are asking about.

One comment to the postulated permanent fields, distributed all other the space due to QED: This postulate is not solvable without a probe body (an experiment). But then such experiment describes the situation, I mentioned above.

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