The magnetic field is often a mystery and a puzzle to people. What is this effect that can operate through empty space and make magnets and metal objects attract or repel each other? What is different about some kinds of materials that make them magnetic when other materials are not? Why is it that running electric current through a coil of wire, as in an electromagnet, generates a magnetic field?
All this is strange, to be sure, though most of us are used to it and don’t think about it much.
However, did you know that magnetic fields are proof that Einstein was right about how distances get shorter and time slows down for moving objects?! Yes, in fact the existence of magnetic fields is a direct consequence of Einstein’s Special Theory of Relativity.
To understand it a bit, visualize one of the basic properties of magnetic fields, namely, that a current carrying wire generates a magnetic field in the space around it. A nearby current carrying wire, or a magnet like a compass needle, feels the effect of the magnetic field as a force pushing or pulling on it. In particular, a nearby wire with a current in the same direction feels an attractive force. Let’s see why.
The first wire can be viewed as being made of two rows of electric charges. There are positive charges (the atoms of the wire) that aren’t moving and the electrons in the wire that are moving. An observer will see that there are equal numbers of positive and negative charges, because the wire is neutrally charged so there is no electric field present.
The nearby current carrying wire is the same thing – a neutrally charged set of stationary positive atoms and moving negative electrons. So, what is the force on this second wire from the first one?
First off, there’s no electrostatic force because the wires are both neutrally charged.
Second, the positive atoms in the second wire are not moving, so we can directly measure the force on these stationary positive charges: namely, no force at all. There’s no electrostatic force because the first wire is uncharged, and there’s no magnetic force because these charges are not moving.
Third, what is the force on the moving electrons in the second wire? Here it’s more complicated. To get the right answer, it’s necessary to imagine moving along with these electrons. Hop aboard one of these electrons and look at what you see. Now, from the vantage point of the second wire, its electrons are stationary and so are the electrons of the nearby first wire. The positive charges of both wires are moving instead in the other direction. Why is there a force on the second wire, then?
What the observer will notice is that the spacing between all the charges is now different. Before, the spacing between positive charges and between negative (moving) charges in both wires was the same. That’s necessary to have no net charge on the wires. Now, however, from the vantage of the moving electrons the spacings are all different. According to Special Relativity, the electrons when they were seen as moving had a distance that was contracted (shorter) than their spacing when stationary. Therefore, the electrons in each wire are now farther apart than they were before. Similarly, as seen from perspective of the (now stationary) electrons in the second wire, the positive charges in the first wire are closer together. This, of course, is because of the relativistic length contraction of the distance between the moving charges. The result of this is that the electrons in the second wire experience a net attractive force from the first wire, because the density of the positive charges is now greater than that of the negative ones. The wire is no longer neutral electrically. The positive charges in the second wire experience no force, because the first wire is neutrally charged in the first reference frame.
When the same analysis is repeated for wires with currents flowing in opposite directions, the resulting force is found to be repulsive instead of attractive, just as expected from a magnetic field analysis.
In Relativity, the forces must be the same in the different reference frames, so there is an attractive force between the two wires. But the magnetic field has disappeared! The attractive force is purely electrostatic in nature! It is due solely to the change in distance between charges between the frame of reference of the room (where a current is seen in the wires) and the frame of reference in which the electrons are at rest.
It is rather curious to note that the actual length contraction (or expansion) is very, very small because the electrons are moving very slowly. Although an electrical current seems to move at nearly the speed of light, in fact the electrons that carry it are only moving at a few millimeters per second. The length contraction is really small, on the order of 1 part in 1021 or 1020 !!! You wouldn’t think that such a small – essentially unmeasurably small – length contraction could have a big effect, but remember that there are a very great many electrons in each wire. The cumulative effect, when calculated exactly (as has been done) accounts exactly for the size and direction of the magnetic field effects.
If the situation is simple enough, you can find a frame of reference where the magnetic field disappears and only the electric field remains. However, it is never possible to find a frame of reference where the electric field disappears and only the magnetic field remains. The upshot is that, in a sense, the magnetic field is a kind of “fictitious” field that is a result solely of electrostatic fields from moving charges.