According to Faraday's Law, what is the relationship between induced emf and the rate of change of flux linkage?

Faraday's Law of electromagnetic induction states that the induced electromotive force (emf) in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. This means that as the rate of change of the magnetic flux increases, the induced emf also increases proportionally. Essentially, if you change the magnetic field strength or the area through which the magnetic field lines pass more quickly, you will generate a greater induced voltage.

This directly proportional relationship can be quantitatively expressed in the formula:

[

\text{emf} = -\frac{d\Phi}{dt}

]

where ( \Phi ) is the magnetic flux and ( dt ) is the time interval over which the change occurs. The negative sign indicates the direction of the induced emf, as described by Lenz's Law, but does not affect the proportionality.

In terms of physical interpretation, if you have a coil of wire and you either increase the strength of an external magnetic field rapidly or move the coil through a magnetic field quickly, you would measure a higher induced voltage, confirming this direct relationship.

Therefore, the understanding of how induced emf relates to the rate of change of flux linkage is fundamental in applications involving electromagnetic induction, such as