Magnetic Force

Two current-carrying wires experience magnetic force based on current direction. When currents flow in the same direction, the wires attract; when opposite, they repel. This force is not electric because the wires are electrically neutral. The interaction arises from the magnetic fields created by moving charges in each wire.

The Lorentz force is the magnetic force on a moving charge Q in a magnetic field B. It equals Q multiplied by the cross-product of velocity v and magnetic field B. This force depends on charge magnitude, field strength, and velocity direction. The right-hand rule determines the force direction relative to velocity and field.

Point your thumb in the current's direction; your wrapped fingers show the magnetic field direction. For upward current, the field points inward into the plane. Concentric loops of magnetic field form around the wire. This rule combines current direction with resulting field orientation to predict magnetic force direction.

Magnetic force is always perpendicular to both velocity and the magnetic field. Since work requires force component parallel to displacement, perpendicular force does zero work. The magnetic force can only change a particle's direction of motion, not its speed. Particle kinetic energy remains constant under magnetic force alone.

First, force magnitude is proportional to charge magnitude. Second, it is proportional to magnetic field strength. Third, magnetic force depends on velocity; stationary charges experience no magnetic force. Fourth, the force is always perpendicular to both velocity and field, distinguishing it from constant electric force.

A compass needle aligns tangentially to concentric circles of magnetic field surrounding the wire. The needle experiences magnetic force from the field created by moving charges in the wire. This demonstrates that magnetic fields are real physical entities that exert forces on magnetic materials and moving charges.

Magnetic force depends on charge velocity; a stationary charge has zero velocity. The Lorentz force equation F = Q(v × B) yields zero when v equals zero. Only moving charges experience magnetic force. This distinguishes magnetic forces from electric forces, which act on charges regardless of motion.