Electromagnetic Field

Recall that the force of a stationary charge is F→ = qE→, but if the charge is moving the force is F→ = qE→ + qv→ × B→. A steady (unchanging in time) current in a wire, generates a magnetic field. Electric current is essentially charges in motion. In an electrical conductor like copper wire, electrons move, while positive charges remain steady. The positive charge cancels the electric charge so the overall charge looks like zero when viewed from outside the wire, so no electric field will exist outside the wire, but the moving charges create a magnetic field from F→ = qv→ × B→ where B→ is the magnetic field vector. The cross product results in magnetic field lines circling the wire. Because of this effect, solenoids (a current-carrying coil of wire that acts as a magnet) can be made by wrapping wire in a tight spiral around a metallic tube, so that the magnetic field inside the tube is linear in direction.

Relating this idea to Newton's first law of motion, which states that for every action there is an equal and opposite reaction, we see that an external magnetic field (from a bar magnet, for example) can exert a force on a current-carrying wire, which will be the sum of the forces on all the individual moving charges in the wire.