Magnetic Force

Consider two wires connected to a battery.

If the currents' directions are opposite, the wires repel. If the directions are the same, the wires attract.

When a test charge is placed nearby, it experiences no force, since the wires are electrically neutral. So, the force acting between the wires is not electric; this is known as the magnetic force.

If a magnetic compass is placed near the wire, the needle experiences a force and is aligned tangentially to a circle around it. As a result, concentric loops of magnetic fields are formed around the wire.

If the thumb points in the current's direction, the wrapped fingers provide the direction of the magnetic field.

For a wire with a current in the upward direction, the magnetic field points inward into the plane, and the magnetic force points to the left.

This combination of directions satisfies the right-hand rule. The magnetic force on a test charge Q moving with velocity v in a magnetic field B is Q multiplied by the cross-product of v and B, called the Lorentz force.