# Faraday's Law: Formula for the Law of Electromagnetic Induction Faraday's law of electromagnetic induction indicates that the induced voltage in a closed circuit is directly proportional to the speed with which the magnetic flux that crosses any surface with the circuit as an edge varies.

The law is named after the physicist and chemist who developed it, Michael Faraday.

In his development, Michael Faraday was based on the principle of conservation of energy. Faraday's hypothesis was that if the flow of an electric current could generate a magnetic field, it would also be possible that the magnetic field could produce an electric current.

## Faraday's Law of Induction Formula

The following formula defines the relationship between the variation of the magnetic flux that passes through a surface S, which is closed by the contour C, and the electric field along the same contour: where

• E represents the electric field.

• B is the magnetic flux density.

• dl is an infinitesimal element of contour C.

• dA is the differential element of the surface S.

With the right hand rule we can know the directions of the contours C and of dA.

In the case of an inductor coil with N turns of the electric wire, it makes N turns, we have the following formula: where

• ε is the induced electromotive force (emf)

• dΦ / dt is the rate of change over time of the magnetic flux Φ.

The negative sign of the formula and the direction of the electromotive force were introduced by Lenz's law.

Faraday's law of induction was the last law to be added to Maxwell's equations

## Examples of Applications of Faraday's Law in Daily Life

Here are some examples of the application of Faraday's law.

### Electric Generator

Electric generators convert rotational kinetic energy into electricity by rotating a magnet called a rotor. The rotor rotates around fixed coils generating a changing magnetic field that induces an electric current.

Depending on the configuration, the current generator can be direct current, alternating current or three phase.

### Electric Motor

The electric motor works in the reverse way as the generator. In an electric motor, a current is applied to an electromagnet that generates a magnetic field. This field interacts with the rotor magnet causing it to rotate.

### Magnetic Brake

A magnetic brake works by connecting an electromagnet to a metal disc.

To activate the brake, we circulate a current through the electromagnet and activate it. The electric current generates a magnetic field on the disk. The magnetic field induces the so-called eddy currents by Faraday's law.

Eddy currents are affected by the Joule effect and release heat, which is energy that comes from the kinetic energy of the disk. By reducing kinetic energy, the puck slows down.

### Induction Cookers

An induction cooker also works by Joule's law generating eddy currents. A spiral magnet is placed under the glass ceramic plate. Placing a metal container on the plate activates the magnet, inducing eddy currents and therefore heat.

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Published: October 16, 2021
Last review: October 16, 2021