Magnetostatics
Magnetostatics studies the steady magnetic fields produced by constant electric currents and permanent magnetization.
Definition
The study of magnetic fields, forces, and potentials arising from steady (time-independent) electric currents and static magnetization, governed by the Biot-Savart law and equivalently by Ampère's law together with the divergence-free nature of the magnetic field.
Scope
Magnetostatics is the branch of electromagnetism dealing with magnetic fields that do not change in time, produced by steady currents or static magnetization. It covers the Biot-Savart law, Ampère's circuital law, the magnetic vector potential, magnetic forces and torques on currents and dipoles, and the response of magnetic materials. It excludes time-varying fields and induction, which belong to full electrodynamics.
Sub-topics
Core questions
- What magnetic field does a given steady current distribution produce?
- How do magnetic forces and torques act on currents and magnetic dipoles?
- Why is there no magnetic charge, and what follows from that?
- How do materials acquire and modify magnetization?
Key concepts
- magnetic field
- steady current
- Biot-Savart law
- Ampère's law
- magnetic vector potential
- magnetic dipole
- permeability
- Lorentz force
Key theories
- Biot-Savart law
- Each current element contributes a magnetic field perpendicular to both the current direction and the line to the field point, falling off as the inverse square of distance; integrating over the circuit gives the total field.
- Ampère's circuital law
- The line integral of the magnetic field around a closed loop equals the enclosed current times the permeability, providing the magnetostatic counterpart of Gauss's law for symmetric current geometries.
- Absence of magnetic monopoles
- No isolated magnetic charges are observed, so the magnetic field is divergence-free and field lines form closed loops; this allows the field to be written as the curl of a vector potential.
Clinical relevance
Magnetostatics underlies electromagnets, magnetic resonance imaging field design, electric motors and generators, magnetic data storage, and magnetic confinement in plasma and accelerator physics.
History
Ørsted's 1820 discovery that a current deflects a compass needle linked electricity to magnetism. Within months Biot and Savart measured the field of a current, and Ampère formulated the force law between currents and the circuital law, establishing magnetostatics as a quantitative science.
Key figures
- Hans Christian Ørsted
- André-Marie Ampère
- Jean-Baptiste Biot
- Félix Savart
Related topics
Seminal works
- jackson1998
- griffiths2017
- purcell2013
Frequently asked questions
- Why are there no magnetic monopoles in magnetostatics?
- No isolated magnetic charge has ever been detected, so magnetic field lines have no sources or sinks and always close on themselves; this is expressed by the magnetic field having zero divergence.
- How is Ampère's law like Gauss's law?
- Both turn a differential field law into a convenient integral relation; Gauss's law relates electric flux to enclosed charge, while Ampère's law relates the circulation of the magnetic field to enclosed current, each simplifying symmetric problems.