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The magnetic field is a relativistic effect

If we consider two charges that move in a rectilinear and uniform way, with the same parallel velocity, as in the picture below, they will suffer from a couple of attractive magnetic forces, because each of them moves in the field produced by the other: the two charges behave as rectilinear wires carrying a continuous electric current in the same direction. Obviously there is also an electric force (repulsive and surely stronger than the magnetic one, at ordinary velocities at least).

two moving charges

Let's imagine now that the motion of the two charges is analyzed by an observer moving at the velocity of the charges: the magnetic effect disappears and the only effect that remains is the electric one, more precisely a normal electrostatic effect. We can imagine that the presence of the magnetic field in the previous reference is only a "relativistic effect". If we add the fact that the "relativistic corrections" are of a size of v2/c2, we can also realize the smallness of this effect: for "ordinary speeds", for instance for the velocity of electrons in a wire carrying a current (about 10-4 m/s), the size of v2/c2 (about10-25) is too small to be measured if at the same time the electric effect is present too. If there had not been some other lucky circumstances, the magnetic field, produced by the charges in motion, would never have been discovered.

Now if we consider two wires and through both of them an electric current moving in the same direction, there is no electric effect (because the effects produced by the positive and the negative charges inside the wires are balanced in an almost perfect way) and so the magnetic is the only acting force. In this case the magnetic force is still due to a relativistic correction of the order of 10-25, but now it is the only existing effect, in consequence of the compensation of the electric effects. So it is possible to measure it because it is not darkened by stronger effects. Magnetism is a consequence of the interaction between electric wires. Now we can conclude that the perfect balancing of the electric effects in wires carrying currents gave us the possibility to reveal the relativistic effects, even at these low speeds, though, obviously, physicists at that time did not know that they were studying just this. For this reason when relativity was discovered there had been no need to modify the laws of electromagnetism: in contrast with mechanics, they were correct to a precision of the order of v2/c2 .

first published on march 11 2002 - last updated on september 01 2003