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Lorentz Force

The electromagnetic force on a charge from local electric and magnetic fields, with a velocity-dependent magnetic contribution.

Version
v1 · 2026-10-31 · History
Domain-specific #
14532
Domain group
Natural Sciences
Origin domain
Physics
Subdomain
Classical Electromagnetism → Physics
Aliases
Lorentz Force Law

Core Idea

The Lorentz force is the force on a charge in electric and magnetic fields: \(\mathbf F=q(\mathbf E+\mathbf v\times\mathbf B)\).[1] The electric term acts even on a stationary charge; the magnetic term depends on motion and is perpendicular to it.[1][2] A pure magnetic field can turn a moving charge without changing its speed, but the combined force need not preserve speed.[2][1]

How would you explain it like I'm…

Electric and Magnetic Pushes

Tiny bits with electric charge get pushed around in two ways. An electric push can shove them even when they're sitting still. A magnetic push only happens when they're moving, and it shoves them sideways, so they curve instead of speeding up. The Lorentz force is the name for both pushes added together.

Electric Push Plus Magnetic Bend

The Lorentz force is the push that electric and magnetic fields put on a charged particle. It has two parts. The electric part pushes the charge even if it isn't moving, and it can speed it up or slow it down. The magnetic part only acts on a moving charge, and it always pushes sideways, at a right angle to the motion, so it bends the path without changing the speed. The same rule explains why a wire carrying current feels a push near a magnet, and how electric motors turn.

Electromagnetic Force Law

The Lorentz force is the total electromagnetic force on a charge q moving with velocity v through electric field E and magnetic field B: F = q(E + v × B). The electric part, qE, acts even on a charge that isn't moving. The magnetic part, qv × B, only exists when the charge moves, and points perpendicular to both the velocity and the field; its size is |q|vB sin θ, where θ is the angle between v and B. Because the magnetic part is always perpendicular to the motion, it does no work and can't change the particle's speed — but the electric part can. The same law, added up over all the moving charges in a wire, explains forces on current-carrying wires and the turning force in motors.

 

The Lorentz force is the electromagnetic force on a charge q moving with velocity v in local fields E and B, F = q(E + v × B). The electric term qE acts regardless of motion, including on a stationary charge. The magnetic term qv × B depends on velocity and is perpendicular to both v and B, with magnitude |q|vB sin θ, where θ is the angle between v and B. Only the magnetic term is necessarily perpendicular to the motion and therefore does no work on the charge; characterizing the whole law as a sideways, speed-preserving force would erase the electric contribution, which can do work. The law applies to an individual charged particle and, by summing forces over mobile charge carriers, to current-carrying conductors. A free particle's trajectory curving in a magnetic field, the force on a wire segment, and the torque on a current loop in a motor are thus different realizations of one charge–field response law, not separate laws tied to particular apparatus.

Scope of Application

  • Free particles: A charge entering a uniform magnetic field perpendicular to its velocity can follow a circular path; motion parallel to the field has no magnetic deflection.[2]

  • Current-carrying conductors: Summed carrier forces can push a wire segment in a magnetic field.[3]

  • Motor loops: Forces on different current-loop segments can produce torque; a working DC motor needs switching hardware as well.[4]

  • Hall strips: Magnetic deflection separates mobile carriers until an induced electric field balances the transverse force.[5]

These cases assume specified fields and a classical charge-motion model.[1][2] The force equation alone does not supply a device's material or mechanical behavior.[1][4]

Clarity

The force law and a direction mnemonic answer different questions. A hand rule helps orient a cross product, but cannot determine force without charge sign, motion and field geometry.[1][2] The “catapult effect” wire picture is a particular illustration; its broad horizontal/away wording is not the general direction law.[6][1]

Manages Complexity

The same local calculation serves a particle, a wire and a loop: evaluate the field force on charges, then aggregate it where the physical system requires.[1][3][4] Geometry, field generation and mechanical constraints remain separate inputs; the equation does not make them disappear.[1][3][4]

Abstract Reasoning

Split the electric term from the velocity-dependent magnetic term, add the vectors, then test motion or force balance.[1] In a Hall strip, an eventual zero transverse net force can coexist with nonzero electric and magnetic components.[5] In a crossed-field selector, only the velocity that balances the opposed contributions passes without lateral deflection under the stated idealization.[5]

Knowledge Transfer

The law transfers literally among charged-particle motion, current-carrying wires, motor loops and Hall measurements because the same charge–field relation recurs.[1][2][3][4][5] A Coriolis term may also involve velocity and a cross product, but it describes motion in a rotating frame rather than electromagnetic force on charge.[7][1] The shared mathematical shape does not make it another Lorentz-force case. The necessary DAG prerequisite is a physical field that supplies local electric or magnetic values, rather than a shared cross-product pattern.

Example

For a charge entering a uniform magnetic field at right angles, with no electric field or other force, \(q\mathbf v\times\mathbf B\) continually bends the trajectory into a circle without changing speed.[2] Here the carrier is one charge, the input is the local field, and velocity sets the magnetic response; no conductor or motor is needed.[2]

Relationships to Other Abstractions

Local relationship map for Lorentz ForceParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Lorentz ForceDOMAINDomain-specific abstraction: Field (physics) — presupposesField (physics)DOMAIN

Current abstraction Lorentz Force Domain-specific

Parents (1) — outgoing typed relations

  • Lorentz Force presupposes Field (physics) Domain-specific

    The Lorentz force law requires pointwise physical electric or magnetic fields to supply E and B at a charged carrier.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Lorentz Force sits in a sparse region of the domain-specific corpus (75th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Physical Quantities, Operators & Formulas (34 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-31

Not to Be Confused With

  • Hall effect: the resulting charge separation and transverse voltage, not the force law itself.[5]

  • Right-hand rule: a directional convention, not an electromagnetic interaction.[1][2]

  • Classical electromagnetism: the larger theory also addresses field sources and evolution.[1]

References

[1] Richard P. Feynman, Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics II (1964), ch.13 (Magnetostatics), §13-1, equation 13.1 and preceding text. Caltech online edition. https://www.feynmanlectures.caltech.edu/II_13.html. First-party full lecture text for the combined Lorentz law and magnetic geometry. registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n

[2] OpenStax, University Physics Volume 2, §11.3, (Motion of a Charged Particle in a Magnetic Field), Figure 11.7 and equations 11.4–11.8. https://openstax.org/books/university-physics-volume-2/pages/11-3-motion-of-a-charged-particle-in-a-magnetic-field. Publisher full text; ideal uniform-field trajectories. registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i

[3] OpenStax, University Physics Volume 2, §11.4, (Magnetic Force on a Current-Carrying Conductor), equations 11.10–11.13 and Example 11.4. https://openstax.org/books/university-physics-volume-2/pages/11-4-magnetic-force-on-a-current-carrying-conductor. Publisher full text; carrier-force aggregation and geometry limits. registry ↩a ↩b ↩c ↩d

[4] OpenStax, University Physics Volume 2, §11.5, (Force and Torque on a Current Loop), opening motor example and Figure 11.15. https://openstax.org/books/university-physics-volume-2/pages/11-5-force-and-torque-on-a-current-loop. Publisher full text; motor setting and required commutation. registry ↩a ↩b ↩c ↩d ↩e

[5] OpenStax, University Physics Volume 2, §11.6, (The Hall Effect), Figure 11.17, equations 11.24–11.25, and Example 11.8. https://openstax.org/books/university-physics-volume-2/pages/11-6-the-hall-effect. Publisher full text; transverse force balance and velocity-selector context. registry ↩a ↩b ↩c ↩d ↩e

[6] “Catapult effect,” Wikipedia revision 1292611258, the exact screened provenance page, https://en.wikipedia.org/w/index.php?oldid=1292611258. Used only to document what the screened source says, not as independent authority for the Lorentz force law. registry ↩

[7] MIT OpenCourseWare, 8.01SC Classical Mechanics, ch.31, “Non-Inertial Linear and Rotating Reference Frames,” especially the rotating-frame summary equation (1.8) and §31.5.3. https://live.ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/mit8_01scs22_chapter31.pdf. University course text; rotating-frame Coriolis cross product and its distinction from physical electromagnetic force. registry ↩