Magnetic Field
The magnetic field is a vector field produced by moving electric charges (currents) and by the intrinsic magnetic moments of particles, exerting force specifically on other moving charges, in a direction perpendicular to both the field and the charge's velocity.
Curious
A compass needle aligning with the Earth's magnetic field, iron filings arranging themselves around a bar magnet, a fridge magnet holding up a piece of paper — all of these are everyday demonstrations of magnetic fields at work. But magnetism has a strange rule electricity doesn't share: it only affects moving charges, and the force it applies is always perpendicular to the direction of motion.
This is why a stationary charged particle sitting next to a magnet feels absolutely nothing — no force at all — while the same particle, once set in motion, suddenly feels a sideways push that curves its path rather than speeding it up or slowing it down.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| F | Magnetic force | newton (N) |
| q | Charge of the moving particle | coulomb (C) |
| v | Velocity of the particle | m/s |
| B | Magnetic field | tesla (T) |
The cross product v × B guarantees the resulting force is always perpendicular to both the particle's velocity and the field direction — this is why a charged particle moving through a uniform magnetic field, with no other forces present, travels in a perfect circle (or a helix, if it has a velocity component along the field direction) rather than a straight line or a curve that changes its speed.
Worked example: A proton moving at 2×10⁶ m/s enters a magnetic field of 0.5 T perpendicular to its velocity. F = qvB = (1.602×10⁻¹⁹)(2×10⁶)(0.5) = 1.602×10⁻¹³ N — this force provides the centripetal force for circular motion, with radius r = mv/(qB) = (1.673×10⁻²⁷)(2×10⁶)/((1.602×10⁻¹⁹)(0.5)) ≈ 0.0418 m ≈ 4.18 cm.
Deep Dive
The full electromagnetic force on a moving charge, combining both electric and magnetic contributions, is given by the Lorentz force law: F = q(E + v × B) — named for Hendrik Lorentz, who gave it its modern, complete form in 1895, unifying the electric and magnetic force contributions into a single expression. This is the fundamental force law of classical electrodynamics, playing a role for electromagnetism analogous to what F = ma plays for classical mechanics generally.
Relativistic origin: In special relativity, the magnetic field is understood not as a separate, independent field from the electric field, but as a relativistic consequence of the electric field as viewed from different reference frames — a charge that produces a pure electric field in its own rest frame produces both electric and magnetic fields when viewed from a frame in which it is moving. This deep connection, made precise by combining Maxwell's equations with special relativity, shows that "electric" and "magnetic" fields are not fully separate phenomena but two aspects of a single electromagnetic field tensor, whose split into electric and magnetic parts depends on the observer's reference frame.
No magnetic monopole (an isolated north or south magnetic "charge," analogous to electric charge) has ever been experimentally observed, consistent with Gauss's law for magnetism (∇·B = 0) — one of Maxwell's four equations.
Concept Relationship Map
Requires: electric charge
Enables: magnetic force, Biot-Savart law
Commonly confused with: electric field (magnetic fields only act on moving charges, and never do work on them)
Sources
- Lorentz, H.A. (1895). Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern. E.J. Brill.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press, Ch. 5.