Lecture

Magnetic Circuits: Inductances and Maxwell Equations

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Description

This lecture covers the concept of magnetic circuits, inductances, and Maxwell's equations, focusing on the quasi-static regime. It explains the relationship between magnetic fields and currents, the analogy between electrical and magnetic circuits, and the calculation of magnetic flux and induced voltage. The lecture also delves into the concept of reluctance and magnetic permeance, as well as the application of the law of induced voltage according to Faraday's law. Various examples and exercises are provided to illustrate the theoretical concepts discussed.

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Ontological neighbourhood

Physics

Electromagnetism: Electrical networks

Related concepts (32)

Magnetic circuit

A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators, transformers, relays, lifting electromagnets, SQUIDs, galvanometers, and magnetic recording heads.

Magnetic reluctance

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the geometry and composition of an object. Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure of the opposition to the electric current. The definition of magnetic reluctance is analogous to Ohm's law in this respect.

Gyrator–capacitor model

The gyrator–capacitor model - sometimes also the capacitor-permeance model - is a lumped-element model for magnetic circuits, that can be used in place of the more common resistance–reluctance model. The model makes permeance elements analogous to electrical capacitance (see magnetic capacitance section) rather than electrical resistance (see magnetic reluctance). Windings are represented as gyrators, interfacing between the electrical circuit and the magnetic model.

Inductance

Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction.

Permeance

Permeance, in general, is the degree to which a material admits a flow of matter or energy. Permeance is usually represented by a curly capital P: . In electromagnetism, permeance is the inverse of reluctance. In a magnetic circuit, permeance is a measure of the quantity of magnetic flux for a number of current-turns. A magnetic circuit almost acts as though the flux is conducted, therefore permeance is larger for large cross-sections of a material and smaller for smaller cross section lengths.

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