31.2: Self-Inductance

Mutual inductance arises when a current in one circuit produces a changing magnetic field that induces an emf in another circuit. On the other hand, self-inductance arises when the current passing through the circuit changes, creating a changing magnetic flux, resulting in inductance in the same circuit.

Consider a circuit connected to an AC source. As the current varies with time, the magnetic flux through the circuit correspondingly changes. Faraday's law tells us that an emf would therefore be induced in the circuit, which will be given by a negative time derivative of the magnetic flux. Since the magnetic field due to a current is directly proportional to the current, the flux due to this field is also proportional to the current. The proportionality constant is known as the self-inductance of the circuit. Similar to mutual inductance, the SI unit of self-inductance is henry.

Self-inductance is associated with the magnetic field produced by a current; any configuration of conductors possesses self-inductance. For example, besides a wire loop, a long, straight wire also has self-inductance, as does a coaxial cable. A coaxial cable is most commonly used by the cable television industry and may also be found connecting your cable modem. Coaxial cables are used due to their ability to transmit electrical signals with minimal distortions. Coaxial cables have two long cylindrical conductors that possess current and a self-inductance that may have undesirable effects.

If the current-carrying wire is made into N number of turns, then the self-inductance is expressed as the ratio of N times the magnetic flux through each turn to the current passing through the loop.

Current flowing in any isolated circuit produces a magnetic field in the circuit. On changing the current, the magnetic flux also changes, inducing an emf.

This emf is called self-induced emf, and the phenomenon is self-inductance.

According to Lenz's law, the self-induced emf opposes any change in the current flowing through the circuit.

Using Faraday's law, the self-induced emf in the circuit can be expressed in terms of magnetic flux.

Also, the magnetic flux in the circuit is proportional to the current flowing through it, and the proportionality constant is known as the self-inductance of the corresponding circuit.

The self-inductance is purely a geometric factor that needs to be calculated separately for all the geometries of the conductor.

Using Faraday's law and the definition of self-inductance, the induced emf can be expressed in terms of self-inductance.

For a straight current-carrying conductor, Ampère's law gives the magnetic field inside the conductor. The magnetic flux is calculated upon integrating the magnetic field over the cross-sectional area. Thus, the self-inductance of the straight current-carrying conductor can be estimated.