What Are Magnetic Forces?

Magnetic forces are the mechanical forces that a magnetic field exerts on moving electric charges, current-carrying conductors, and magnetic materials. They differ fundamentally from electric forces in that they act perpendicular to the velocity of a moving charge and can therefore change a particle's direction without doing work on it. The governing expression is the Lorentz force law: F = q(E + v × B), where q is the charge, v the velocity, E the electric field, and B the magnetic flux density. The magnetic component of this force, qv × B, is the origin of almost all electromagnetic actuation, from the rotation of an electric motor to the deflection of an electron beam in a cathode ray tube.

The study of magnetic forces spans classical electrodynamics, materials physics, and mechanical engineering. Quantifying these forces accurately requires knowledge of both the field distribution and the properties of the medium in which the force acts.

The Lorentz Force and Magnetostatic Forces

For a straight conductor of length L carrying current I in a uniform field B, the force simplifies to F = IL × B, directed perpendicular to both the conductor and the field. This expression governs the torque in DC motors, the deflecting force in moving-coil galvanometers, and the thrust in linear induction motors. Physics LibreTexts on the Lorentz force presents the full vector treatment and shows how the cross-product geometry means the force is always normal to the velocity, confirming that magnetic forces alone cannot change the kinetic energy of a charged particle. Magnetostatic forces between current loops, such as the attraction between two parallel conductors carrying current in the same direction, underlie the ampere definition in the SI system and are used in precision force balances for electrical metrology.

Coercive Force and Magnetic Hardness

Coercive force, or coercivity (Hc), is the magnitude of the reverse magnetic field intensity required to drive the remanent magnetization of a previously saturated material back to zero. It is a material property read directly from the hysteresis loop and determines whether a magnetic material is classified as magnetically soft or magnetically hard. Soft materials such as annealed silicon steel have coercivities below 1 A/m, making them easy to magnetize and demagnetize repeatedly for use in transformer cores and motor laminations. Hard materials such as sintered neodymium-iron-boron (Nd₂Fe₁₄B) have coercivities exceeding 1,000 kA/m, enabling them to resist demagnetization in the stray fields present inside motors and loudspeakers. The coercive force is an intrinsic indicator of the energy required to reverse domain alignment, and its engineering is central to permanent magnet design.

Electromagnetic Actuators

Electromagnetic actuators convert electrical energy into mechanical force or displacement by exploiting the Lorentz force or the reluctance force acting on a magnetically permeable armature. Voice-coil actuators in hard disk drive head-positioning assemblies and loudspeaker drivers are Lorentz-force devices: a current-carrying coil sits in a radial gap field provided by a permanent magnet, and the axial force is proportional to the product of current and flux density. A PMC study of a two-degree-of-freedom Lorentz force actuator demonstrates how careful coil-and-magnet geometry enables simultaneous vertical and horizontal force generation for precision positioning platforms. Reluctance actuators, by contrast, pull a magnetically soft armature toward a region of lower magnetic reluctance, generating forces that depend on the square of the flux density and are therefore less linear but capable of very large forces at small gaps.

Applications

Magnetic forces have applications across a wide range of engineering disciplines, including:

• Electric motors and generators, where Lorentz forces on rotor conductors produce shaft torque
• Magnetic bearings, where controlled reluctance and Lorentz forces support rotating shafts without mechanical contact
• Particle accelerators, where bending and focusing magnets steer beams using transverse magnetic force
• Loudspeakers and hard disk drive actuators, where voice-coil mechanisms provide precise linear displacement
• Magnetic braking systems, where eddy-current-induced forces provide contactless deceleration in trains and laboratory equipment