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Mutual inductance is a fundamental concept in the field of electromagnetism, a subfield of physics. It describes the ability of one electrical circuit to induce a voltage in another due to changes in magnetic field. The inductances of the two circuits and their coupling coefficient come into play in understanding and calculating mutual inductance.

Mutual Inductance (M) = |

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The formula for mutual inductance (M) between two coils is given by:

M = k × sqrt(L_{1} × L_{2})

Where:

- M: Mutual Inductance
- k: Coupling Coefficient, a dimensionless parameter between 0 and 1 indicating how closely the two circuits are coupled
- L
_{1}: Inductance of coil 1 - L
_{2}: Inductance of coil 2

The mutual inductance formula is derived from the basic principles of electromagnetism. The concept of mutual inductance was first introduced by Michael Faraday in 1831, and the formulation has been refined by physicists and electrical engineers over the years. It is integral to the study and application of electromagnetic phenomena.

Mutual inductance plays a crucial role in the design and operation of many electrical and electronic devices. Transformers, for example, work on the principle of mutual inductance, with an alternating current in the primary coil inducing a voltage in the secondary coil.

Michael Faraday, one of the most influential scientists in the history of physics, first discovered electromagnetic induction, including mutual inductance. His pioneering work in the 19th century set the foundation for the field of electromagnetism and paved the way for the technological revolution that followed.

- The concept of mutual inductance is central to many modern technologies, from electric power transmission to wireless charging systems.
- Understanding and manipulating mutual inductance has been a key factor in advancing electrical power systems and electronics over the years.
- The unit of mutual inductance in the International System of Units is the henry (H), named after the American physicist Joseph Henry who also conducted significant work in electromagnetism.

Understanding mutual inductance is vital in physics and electrical engineering. This concept not only underscores fundamental electromagnetic interactions but also has extensive practical applications. It is integral to the operation of a wide range of electrical devices and systems that are central to our modern world.

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