How does the change in magnetic flux relate to the induced EMF?

The induced EMF is directly proportional to the rate of change of magnetic flux.

When there is a change in magnetic flux, an electromotive force (EMF) is induced in a conductor. This is known as electromagnetic induction. The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux. This is given by Faraday's law of electromagnetic induction.

Faraday's law states that the induced EMF is equal to the negative rate of change of magnetic flux. Mathematically, this can be expressed as E = -dΦ/dt, where E is the induced EMF, Φ is the magnetic flux, and t is time. The negative sign indicates that the induced EMF opposes the change in magnetic flux that produced it.

The magnetic flux is the product of the magnetic field strength and the area perpendicular to the magnetic field. Therefore, the rate of change of magnetic flux can be increased by changing the magnetic field strength, the area, or the angle between the magnetic field and the area. This can be achieved by moving a magnet towards or away from a conductor, rotating a coil in a magnetic field, or changing the current in a nearby conductor.

In summary, the induced EMF is directly proportional to the rate of change of magnetic flux, according to Faraday's law of electromagnetic induction. This relationship is fundamental to many applications of electromagnetic induction, such as generators, transformers, and motors.