Derivation of self inductance formula: solenoid self inductance formula using Faraday's Law.

Описание: Derivation of self inductance formula and example of induced emf when a solenoid is disconnected.

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We start by motivating the idea of self-inductance: when a solenoid current turns on, this introduces magnetic flux through the coils, and the change in flux creates an induced emf to counteract the change. To quantify the induced emf and find the solenoid self inductance formula, we use Faraday's law expressing the induced emf in terms of the rate of change in flux.

We incorporate the solenoid formula for the magnetic field in terms of current, and then we can express the induced emf in terms of the rate of change in current. The coefficient in this formula is the inductance, or self-inductance of the solenoid. The bigger the self-inductance, the greater the resistance to change in current.

We wrap up the inductance formula solenoid self inductance introduction by working an example in which a solenoid of known length, number of turns, average diameter and initial current is suddenly disconnected, inducing an emf that tries to maintain the original current.;