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How does Faraday’s law explain the production of electric current by a changing magnetic field?

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Diagram showing a circular loop of wire with an electric current, surrounded by curved blue lines representing magnetic field lines that loop around the wire and pass through its center. — magnetism Some lines of the magnetic field B (blue) for an electric current I (gold) in a loop.

Faraday’s law of induction explains that an electric current is produced in a circuit when there is a change in the magnetic flux passing through it. This phenomenon, known as electromagnetic induction, occurs because a changing magnetic field induces an electromotive force (emf) within the conductor.12

The magnitude of this induced emf is directly proportional to the rate at which the magnetic flux changes over time, expressed by the equation:
$e m f = - \frac{d Φ}{d t}$
In this formula, $Φ$ represents the magnetic flux and $t$ represents time. The negative sign in the equation is a result of Lenz’s law, which dictates that the induced current flows in a direction that opposes the change in the magnetic field that created it, thereby upholding the conservation of energy.13

Essentially, whether by moving a magnet near a coil or varying the current in an electromagnet, the resulting change in magnetic lines of force cutting across the circuit drives the flow of electric charge.14