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

When a conductor moves through a magnetic field or when the magnetic field changes around a conductor, an EMF is induced in the conductor. The magnitude of this induced EMF is directly proportional to the rate of change of magnetic flux. This is known as Faraday's law of electromagnetic induction.

Magnetic flux is the product of the magnetic field strength and the area perpendicular to the field. The rate of change of magnetic flux is the change in magnetic flux over time. This can occur due to a change in the magnetic field strength, a change in the area of the conductor perpendicular to the field, or a change in the angle between the conductor and the field.

The induced EMF can be calculated using the equation EMF = -dΦ/dt, where EMF is the induced electromotive force, Φ is the magnetic flux, and t is time. The negative sign indicates that the induced EMF opposes the change in magnetic flux.

In practical applications, this relationship is used in devices such as generators and transformers. By varying the rate of change of magnetic flux, the induced EMF can be controlled to produce a desired output voltage or current. Understanding the relationship between magnetic flux and induced EMF is crucial in the study of electromagnetism.

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