Derivation of mutual induction
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electromagnetism and electronics, inductance is the property of an electrical conductor by which a change in electric current through it induces an electromotive force (voltage) in the conductor. It is more accurately called self-inductance. The same property causes a current in one conductor to induce an electromotive force in nearby conductors; this is called mutual inductance.[1]
Inductance is an effect caused by the magnetic field of a current-carrying conductor acting back on the conductor. An electric current through any conductor creates a magnetic field around the conductor. A changing current creates a changing magnetic field. From Faraday's law of induction any change in magnetic flux through a circuit induces an electromotive force (voltage) across the circuit. Inductance is the ratio {\displaystyle L} L between this induced voltage {\displaystyle v} v and the rate of change of the current {\displaystyle i(t)} i(t) in the circuit
{\displaystyle v=L{di(t) \over dt}} {\displaystyle v=L{di(t) \over dt}}
From Lenz's law, this induced voltage, or "back EMF", will be in a direction so as to oppose the change in current which created it. Thus inductance is a property of a conductor which opposes any change in current through the conductor. An inductor is an electrical component which adds inductance to a circuit. It typically consists of a coil or helix of wire.
The term inductance was coined by Oliver Heaviside in 1886.[2] It is customary to use the symbol {\displaystyle L} L for inductance, in honour of the physicist Heinrich Lenz.[3][4] In the SI system, the unit of inductance is the henry (H), which is the amount of inductance which causes a voltage of 1 volt when the current is changing at a rate of one ampere per second. It is named for Joseph Henry, who discovered inductance independently of Faraday.[5]
Electric circuits which are located close together, so the magnetic field created by the current in one passes through the other, are said to be inductively coupled. A change in current in one circuit will cause the magnetic flux through the other circuit to vary, which will induce a voltage in the other circuit, by Faraday's law. The ratio of the voltage induced in the second circuit to the rate of change of current in the first circuit is called the mutual inductance {\displaystyle M} M between the circuits. It is also measured in henries.
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