>>12221055consider two parallel metal wires with current flowing in them (like when you first studied magnetism).
in the rest frame of the wires everything appears to be electrically neutral, with a stationary lattice of positively charged metal ions and moving conduction electrons. since there is no net charge anywhere, there appears to be no electric force. however we know from experiment that if the current in the wires flows in the same direction the wires attract, and if they flow in opposite directions they repel. we attribute this to a magnetic force.
however, consider what the electrons see in their rest frames. suppose the current flows the same direction. in this case, an electron on one wire moves at the same velocity as an electron on the other, and since there is no difference in velocity, there are no length contraction effects, so both wires carry equal negative charge density. however the metal ions are moving w.r.t the electrons, and length contraction indicates that there will apparently be a higher positive charge density than negative. in other words, the wires appear to be positively charged, and thus the electrons feel an attractive electrical force to the other wire. the wires attract, just like when you introduce a magnetic force.
the other situation is current flowing in opposite directions. in this case everything is still neutral in the wire rest frame. when you consider the electrons rest frame in one of the wire, the other wire will still appear to have greater positive charge density than the rest frame, but since the electrons are going in the opposite direction, they have an even higher negative charge density due to length contraction. the end result is the electron on one wire sees the other wire as negatively charge. thus the wires repel. the same result as in magnetism.
thus you can see the magnetic force is actually due to relativistic effects and the electric force.
