Electromagnetic induction is a phenomenon in physics where a changing magnetic field induces an electromotive force (EMF) or voltage in a conductor. This principle was first discovered by Michael Faraday in 1831 and later formulated by him and Joseph Henry.

The key points of electromagnetic induction include:

## Faraday's Law of Electromagnetic Induction:

This law 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. Mathematically, it can be expressed as:

$\text{EMF}=-\frac{\ufffd\mathrm{\Phi}}{\ufffd\ufffd}$
where:

- $\text{EMF}$ is the induced electromotive force,
- $\frac{\ufffd\mathrm{\Phi}}{\ufffd\ufffd}$ is the rate of change of magnetic flux.

The negative sign indicates the direction of the induced current according to Lenz's Law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

**Relation Between Magnetism and Electricity:**

This relationship is described by Maxwell's equations, which demonstrate how changes in electric fields can induce magnetic fields and vice versa. This forms the basis of electromagnetism.

**Production of Induced E.M.F. and Current:**

When there is a change in magnetic flux within a closed loop, an electromotive force (EMF) is induced, leading to the production of an electric current according to Faraday's law of electromagnetic induction.

**Faraday’s Laws of Electromagnetic Induction:**

Faraday's laws state that the magnitude of the induced EMF is proportional to the rate of change of magnetic flux and is inversely proportional to the time over which the change occurs. Faraday's laws are fundamental to understanding electromagnetic induction.

**The direction of Induced E.M.F. and Current:**

The direction of the induced EMF and current is determined by Lenz's law, which states that the induced current will always flow in a direction that opposes the change in magnetic flux that produced it.

**Lenz’s Law:**

Lenz's law is a consequence of the conservation of energy and specifies the direction of the induced current in a closed loop due to a changing magnetic field. It ensures that the induced current works against the change in magnetic flux.

**Induced E.M.F.:**

Induced electromotive force is the voltage generated in a coil due to a change in magnetic flux through the coil.

**Dynamically-induced E.M.F.:**

This refers to the induced EMF when there is relative motion between a coil and a magnetic field.

**Statically-induced E.M.F.:**

This refers to the induced EMF when there is a change in the magnetic field without any physical motion, such as when the magnetic field strength changes.

**Self-Inductance:**

Self-inductance is a property of a coil or conductor that induces an electromotive force in itself when the current through it changes.

**Coefficient of Self-Inductance (L):**

The coefficient of self-inductance, denoted by L, quantifies the degree of self-induction in a coil.

**Mutual Inductance:**

Mutual inductance occurs when the changing current in one coil induces an electromotive force in another nearby coil.

**Coefficient of Mutual Inductance (M):**

The coefficient of mutual inductance, denoted by M, measures the strength of the mutual inductive coupling between two coils.

**Coefficient of Coupling—Inductances in Series:**

The coefficient of coupling represents the degree of magnetic coupling between two inductors in series.

**Inductances in Parallel:**

When inductors are connected in parallel, the total inductance is determined by their individual values and their coupling coefficient.

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