How does a change in magnetic flux induce voltage?

A change in magnetic flux induces voltage through a process known as electromagnetic induction.

Electromagnetic induction is a fundamental principle in physics, discovered by Michael Faraday in 1831. It describes the process by which a change in magnetic flux can generate an electromotive force (EMF), or voltage. This principle is the basis for many technologies we use today, including electric generators and transformers.

The magnetic flux through a loop of wire changes when the magnetic field changes, the area of the loop changes, or the angle between the magnetic field and the normal to the loop changes. When this happens, Faraday's law of electromagnetic induction states that the induced EMF in the loop is equal to the rate of change of the magnetic flux through the loop. This can be mathematically represented as E = -dΦ/dt, where E is the induced EMF, Φ is the magnetic flux, and t is time.

The negative sign in Faraday's law represents Lenz's law, which states that the induced EMF and hence the induced current in a loop is always in such a direction as to oppose the change in magnetic flux producing it. This is a manifestation of the conservation of energy. The induced current will create its own magnetic field, which will oppose the change in the original magnetic field.

The magnitude of the induced EMF depends on how quickly the magnetic flux changes. If the magnetic field changes rapidly, a larger EMF is induced. Similarly, if the loop is larger or there are more turns in the coil, the change in magnetic flux and hence the induced EMF will be larger.

In summary, a change in magnetic flux induces voltage through the process of electromagnetic induction. This is described by Faraday's law and involves the generation of an EMF that opposes the change in magnetic flux, as per Lenz's law. The magnitude of the induced EMF depends on the rate of change of the magnetic flux and the characteristics of the loop.