Maxwell's equations

Maxwell's equations are a set of four differential equations that describe how electric and magnetic fields interact. They were first presented by James Clerk Maxwell, a Scottish physicist, in the 19th century. These equations form the foundation of classical electrodynamics, optics, and electric circuits.

History

The equations were first published by Maxwell in his 1865 paper "A Dynamical Theory of the Electromagnetic Field". They were derived using the experimental results of other scientists like Michael Faraday, André-Marie Ampère, and Carl Friedrich Gauss.

Equations

Maxwell's equations can be written in two forms: the "integral form" and the "differential form". The integral form is more intuitive and easier to understand, while the differential form is more useful for calculations.

Integral form

The integral form of Maxwell's equations is:

1. Gauss's law for electricity: The electric flux through any closed surface is proportional to the total charge enclosed by the surface.
2. Gauss's law for magnetism: The magnetic flux through any closed surface is zero.
3. Faraday's law of induction: The electromotive force around a closed path is equal to the rate of change of the magnetic flux through the surface bounded by the path.
4. Ampère's law with Maxwell's addition: The magnetic field around a closed path is equal to the total current (including displacement current) through the surface bounded by the path.

Differential form

The differential form of Maxwell's equations is:

1. Gauss's law for electricity: The divergence of the electric field is equal to the charge density.
2. Gauss's law for magnetism: The divergence of the magnetic field is zero.
3. Faraday's law of induction: The curl of the electric field is equal to the negative rate of change of the magnetic field.
4. Ampère's law with Maxwell's addition: The curl of the magnetic field is equal to the current density plus the rate of change of the electric field.

Applications

Maxwell's equations have wide-ranging applications in various fields of physics and engineering. They are used in the design of electrical circuits, antennas, and electric power generation and transmission systems. They also form the basis of the theory of light and other electromagnetic waves.

See also

• Electromagnetic field
• Electromagnetic radiation
• Electromagnetic wave equation
• Lorentz force

References

Maxwell's equations Resources
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