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Category# Magnetostatics

Summary

Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static – as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic storage devices as in computer memory.
Starting from Maxwell's equations and assuming that charges are either fixed or move as a steady current , the equations separate into two equations for the electric field (see electrostatics) and two for the magnetic field. The fields are independent of time and each other. The magnetostatic equations, in both differential and integral forms, are shown in the table below.
Where ∇ with the dot denotes divergence, and B is the magnetic flux density, the first integral is over a surface with oriented surface element . Where ∇ with the cross denotes curl, J is the current density and H is the magnetic field intensity, the second integral is a line integral around a closed loop with line element . The current going through the loop is .
The quality of this approximation may be guessed by comparing the above equations with the full version of Maxwell's equations and considering the importance of the terms that have been removed. Of particular significance is the comparison of the term against the term. If the term is substantially larger, then the smaller term may be ignored without significant loss of accuracy.
A common technique is to solve a series of magnetostatic problems at incremental time steps and then use these solutions to approximate the term . Plugging this result into Faraday's Law finds a value for (which had previously been ignored).

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Related concepts (3)

Ampère's force law

In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field, following the Biot–Savart law, and the other wire experiences a magnetic force as a consequence, following the Lorentz force law.

Horseshoe magnet

A horseshoe magnet is either a permanent magnet or an electromagnet made in the shape of a horseshoe (in other words, in a U-shape). The permanent kind has become the most widely recognized symbol for magnets. It is usually depicted as red and marked with ′North' and 'South' poles. Although rendered obsolete in the 1950s by squat, cylindrical magnets made of modern materials, horseshoe magnets are still regularly shown in elementary school textbooks.

Biot–Savart law

In physics, specifically electromagnetism, the Biot–Savart law (ˈbiːoʊ_səˈvɑr or ˈbjoʊ_səˈvɑr) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and consistent with both Ampère's circuital law and Gauss's law for magnetism.

Related categories (7)

Phase transitions

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.

Electrodynamics

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena.

Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems.