Faraday’s law

Faraday's law refers to two related principles in electromagnetism, both formulated by the English scientist Michael Faraday:

Faraday's First Law of Electromagnetic Induction:

The induced electromotive force (EMF) in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit.

\(\varepsilon = -\frac{d\Phi}{dt}\)\( \)

\(\Phi_B\) represents the magnetic flux, which is the measure of the magnetic field B passing through a surface. The magnetic flux \(\Phi_B\) through a surface is mathematically defined as the dot product of the magnetic field vector \(\vec{B}\) and a vector representing the surface area \(\vec{A}\)(perpendicular to the surface).

\[\Phi_B = \vec{B} \cdot \vec{A}\]

The time rate of change of this magnetic flux \((-d\Phi_B/dt)\) induces an electromotive force (EMF) in a closed loop, as described by the equation:

\[\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_B}{dt} \]

This relationship highlights how a changing magnetic field induces an electric field and subsequently an EMF in a closed circuit. The negative sign indicates that the induced EMF opposes the change in magnetic flux.

The integral on the left is performed around a closed path that forms the boundary of the surface.

E is the electric field induced by the change in flux. The integral on the left is the induced electromotive force (emf) around the closed path. If there is an induced emf around the path, and if the material has some conductivity, currents will flow to oppose the change in flux.

Explanation: When the magnetic field through a closed loop changes over time, it induces an electromotive force, causing an electric current to flow in the circuit. The negative sign indicates that the induced EMF opposes the change in magnetic flux.

Faraday's Second Law of Electrolysis:

The mass of a substance deposited or liberated during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

\[m \propto Q\]

Explanation: This law relates the amount of chemical reaction occurring during electrolysis to the electric charge passed through the electrolyte. It provides a quantitative relationship between the amount of material deposited or liberated and the charge passed.

Faraday's laws are fundamental in understanding electromagnetic induction and the principles underlying various electrical and electrochemical processes. These laws have wide applications in fields such as power generation, transformers, and electrochemistry.