Magnetic Force
The magnetic force is the force exerted by a magnetic field on a moving charge or, equivalently, on a current-carrying conductor — since current is simply many moving charges collectively — always directed perpendicular to both the current (or velocity) and the field.
Curious
A single moving charge feels the magnetic force F = qv×B. A wire carrying a current is really just an enormous number of moving charges (electrons) travelling together, so the total force on the wire is simply the sum of the tiny forces on every one of those moving charges — which works out to a clean, practical formula for the force on a length of current-carrying wire.
This force is precisely what makes electric motors spin: a current-carrying loop of wire, placed in a magnetic field, experiences forces on opposite sides of the loop pointing in opposite directions, creating a torque that rotates the loop — repeated continuously (with clever current-reversal via a commutator or electronic switching) to produce continuous rotation.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| F | Force on the wire | newton (N) |
| I | Current | ampere (A) |
| L | Length vector of wire (direction of current flow) | metre (m) |
| B | Magnetic field | tesla (T) |
Worked example: A straight wire of length 0.3 m carries a current of 5 A, oriented perpendicular to a magnetic field of 0.8 T. F = ILB = (5)(0.3)(0.8) = 1.2 N.
Deep Dive
André-Marie Ampère's early 19th-century experiments established that two parallel current-carrying wires exert forces on each other — attractive if the currents flow in the same direction, repulsive if opposite — a result that directly follows from combining the Biot-Savart law (giving the field created by one wire) with the force law F = IL×B (giving the force that field exerts on the other wire). This mutual force between currents is, in fact, the modern basis for defining the ampere itself in terms of a precisely specified force between parallel wires (prior to the 2019 SI redefinition, which now defines the ampere via a fixed elementary charge instead).
Torque on a current loop: For a planar current loop of area A carrying current I in a uniform field B, the net force on the loop is zero (forces on opposite sides cancel), but there is generally a net torque τ = IA × B (equivalently τ = m × B, where m = IA is the loop's magnetic dipole moment) — this torque, not a net force, is what drives every electric motor's rotation.
Concept Relationship Map
Requires: magnetic field
Enables: electric motor operation, Biot-Savart law
Commonly confused with: force direction being "along" the field or current rather than perpendicular to both
Sources
- Ampère, A.M. (1827). Mémoires de l'Académie Royale des Sciences.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press, Ch. 5.