The electromotive force (EMF) induced in a coil is directly proportional to the rate of change of magnetic flux through that coil.

According to Faraday’s law of electromagnetic induction, when a coil is exposed to a varying magnetic field, an EMF is generated within the coil. The magnitude of this induced EMF is directly proportional to how quickly the magnetic flux changes. In practical terms, this means that if the magnetic field changes rapidly, the induced EMF will be larger compared to a scenario where the magnetic field changes more slowly.

The rate of change of magnetic flux can be enhanced by several factors: increasing the strength of the magnetic field, increasing the number of turns in the coil, or accelerating the rate at which the magnetic field changes. Conversely, if the rate of change of magnetic flux decreases, the resulting induced EMF will also diminish.

This fundamental relationship between the rate of change of magnetic flux and the induced EMF is crucial in various applications, including generators and transformers. In a generator, for instance, a coil is rotated within a magnetic field to create a changing magnetic flux, thereby generating an EMF. In a transformer, two coils are positioned near each other; a changing current in one coil generates a varying magnetic field that induces an EMF in the adjacent coil.

In summary, the induced EMF in a coil is directly proportional to the rate of change of magnetic flux through the coil. This relationship plays a vital role in many applications of electromagnetic induction.