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I've read that both the electric and magnetic field vectors are perpendicular to each other in an electromagnetic wave.

Passing steady current through a straight conductor shows some magnetic flux (because most of the energy is wasted into outer space as magnetic lines). But, when it is passed through a helical coil such as the solenoid or even an inductor, a steady magnetic field is produced along the axis of the coil. Hence, both magnetic and electric fields are related to each other.

How is this actually happening? Can one field be always produced by the other? An explanation focusing on Electric and magnetic fields would be appreciated.

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Passing a steady current through a straight conductor does produce a magnetic field. The field lines are circular, looping around the current according to the right hand rule. hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html –  Benjamin Hodgson Aug 13 '12 at 14:39
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The short answer is "Maxwell's equations", and the long answer is "Take a introductory E&M course". –  dmckee Aug 13 '12 at 14:55
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What kind of answer do you expect to "How is this possible?"? Seriously, why do you think it wouldn't be "possible"? Moreover, if you've taken a intro course then you should be aware that this is an experimental fact, right? No amount of philosophy can trump that. That which is, is. –  dmckee Aug 13 '12 at 16:06
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@CrazyBuddy, you seem to be asking "How are Maxwell's equations possible?". If you are asking something different, please edit your question for clarity. However, if that is what you're asking, you might as well ask "how is it possible the Universe is what it is?" and that's not a physics question if it is even a valid question at all. –  Alfred Centauri Aug 13 '12 at 16:23
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While I think your question may be problematic to some because they are very weary of the "why" question, because physics can only go so deep, I recognize that it is hard to just accept a causal relationship between things that seem arbitrarily related, so lets try to look deeper.

A magnetic field is caused by a moving electric charge correct? The moving electric charge causes an increase in the electric field in front of it and a decrease in the electric field in back of it, and these changes create a magnetic field, but let's go back to the charge.

Let's imagine that this charge is moving extremely fast, at relativistic speeds even. Next to it and parallel to its motion is an infinitely long wire with current flowing through it, a lot of current too. Let's say that the electrons in this wire are moving just as fast as the electron, and in the same direction. We could even imagine them with race helmets on, racing each other off to infinity.

Now this wire is electrically neutral, for every electron in the wire there is a proton, so the electron traveling alongside should feel no pull towards the wire or a push away. However, this is all from our perspective. To us the electrons are moving fast, but what about to them?

According to relativity, they have every right to say that they are not moving. What looked like racing hats to us were actually top hats, and they were sitting down having some tea while we zoomed by at nearly the speed of light. Now we would look sort of funny, because the effects of relativity cause us to look squashed. This is important, because we would not be the only things zooming past the electrons.

The protons in the wire as well would be zooming past them as well. The same relativistic squashing happens with them, but this time it's more important. The relativistic length contraction not only squishes the protons, but because it is a whole column of protons moving past them, the column squishes as well, increasing the positive charge density of the wire. The electron feels the effect of this increased charge density as a pull inwards and so it drifts closer to the wire.

We see this in our frame as well and are perplexed, why would the electron feel a pull from the wire? We see no excess charge in the wire, so we ascribe this effect to a different force, the magnetic force. However, from the electrons reference frame, this behavior is perfectly normal, the protons moving past him are closer together than the electrons standing still and the electric force from the wire pull him closer.

This is kind of what magnetism is, electricity's compensation for relativity. For if magnetism didn't exist, we would see the electron attracted to the wire, for no explainable reason. Magnetism is sort of the relativistic form of electricity.

As for them interacting and causing each other, this must happen or else other laws of physics could possibly be broken (or you would have a meaningless thing like a force from nothing). This is a comforting example of how a part of physics holds itself up by itself.

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