Inductance

Understanding the unity of these forces of nature, and the scientific theory of electromagnetism was initiated and achieved during the 19th century.

He expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side.

For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead ("Faraday's disk").

through a circuit is equal to the product of the perpendicular component of the magnetic flux density and the area of the surface spanning the current path.

By Faraday's law of induction, any change in flux through a circuit induces an electromotive force (EMF,

The negative sign in the equation indicates that the induced voltage is in a direction which opposes the change in current that created it; this is called Lenz's law.

The inductance of a circuit depends on the geometry of the current path, and on the magnetic permeability of nearby materials; ferromagnetic materials with a higher permeability like iron near a conductor tend to increase the magnetic field and inductance.

An inductor is an electrical component consisting of a conductor shaped to increase the magnetic flux, to add inductance to a circuit.

The inductance is proportional to the square of the number of turns in the coil, assuming full flux linkage.

The inductance of a coil can be increased by placing a magnetic core of ferromagnetic material in the hole in the center.

The energy from the external circuit required to overcome this "potential hill" is stored in the increased magnetic field around the conductor.

If ferromagnetic materials are located near the conductor, such as in an inductor with a magnetic core, the constant inductance equation above is only valid for linear regions of the magnetic flux, at currents below the level at which the ferromagnetic material saturates, where the inductance is approximately constant.

If the magnetic field in the inductor approaches the level at which the core saturates, the inductance begins to change with current, and the integral equation must be used.

[21] It is defined analogously to electrical resistance in a resistor, as the ratio of the amplitude (peak value) of the alternating voltage to current in the component

In an example from everyday experience, just one of the conductors of a lamp cord 10 m long, made of 18 AWG wire, would only have an inductance of about 19 μH if stretched out straight.

However, for a typical coaxial line application, we are interested in passing (non-DC) signals at frequencies for which the resistive skin effect cannot be neglected.

Most practical air-core inductors are multilayer cylindrical coils with square cross-sections to minimize average distance between turns (circular cross -sections would be better but harder to form).

The circuit voltage for a nonlinear inductor is obtained via the differential inductance as shown by Faraday's Law and the chain rule of calculus.

This is the generalized case of the paradigmatic two-loop cylindrical coil carrying a uniform low frequency current; the loops are independent closed circuits that can have different lengths, any orientation in space, and carry different currents.

Nonetheless, the error terms, which are not included in the integral are only small if the geometries of the loops are mostly smooth and convex: They must not have too many kinks, sharp corners, coils, crossovers, parallel segments, concave cavities, or other topologically "close" deformations.

and we ignore the effect of the retarded time (assuming the geometry of the circuits is small enough compared to the wavelength of the current they carry).

Multiplying the equation for vm above with imdt and summing over m gives the energy transferred to the system in the time interval dt,

It is helpful to associate changing electric currents with a build-up or decrease of magnetic field energy.

The rate of change of velocity (current) multiplied with mass (inductance) requires or generates a force (an electrical voltage).

[29] Mutually coupled inductors can be described by any of the two-port network parameter matrix representations.

Alternatively, two coupled inductors can be modelled using a π equivalent circuit with optional ideal transformers at each port.

The amount of mutual inductance between the two windings, together with the Q factor of the circuit, determine the shape of the frequency response curve.

Stongly-coupled self-resonant coils can be used for wireless power transfer between devices in the mid range distances (up to two metres).

[34] Strong coupling is required for a high percentage of power transferred, which results in peak splitting of the frequency response.

The table below lists formulas for the self-inductance of various simple shapes made of thin cylindrical conductors (wires).