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Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.

### Conceptual descriptions

### Formulation in terms of electric and magnetic fields (microscopic or in vacuum version)

### Relationship between differential and integral formulations

### Vacuum equations, electromagnetic waves and speed of light

### Macroscopic formulation

### Alternative formulations

### Relativistic formulations

### Solutions

### Overdetermination of Maxwell's equations

### Maxwell's equations as the classical limit of QED

### Variations

### Historical publications