Maxwell's equations are four fundamental equations that describe electromagnetic fields and their interactions with matter. These equations unify electricity, magnetism, and light into a single theory of electromagnetism. They show how electric and magnetic fields are interconnected and how they propagate through space as electromagnetic waves.
Maxwell's equations consist of four fundamental laws. First, Gauss's law for electricity states that electric charges create electric fields. The divergence of the electric field is proportional to the charge density. Second, Gauss's law for magnetism states that there are no magnetic monopoles - the divergence of the magnetic field is always zero.
The third equation is Faraday's law, which states that changing magnetic fields create electric fields. The curl of the electric field equals the negative time derivative of the magnetic field. The fourth equation is Ampère-Maxwell law, showing that electric currents and changing electric fields create magnetic fields. Together, these equations demonstrate the deep connection between electricity and magnetism.
Maxwell's equations predict the existence of electromagnetic waves. These waves travel at the speed of light, which equals one over the square root of mu naught epsilon naught. This revealed that light itself is an electromagnetic wave! These waves include radio waves, microwaves, X-rays, and visible light, all traveling at the same speed in vacuum.
To summarize what we've learned: Maxwell's equations are four fundamental laws that unify electricity, magnetism, and light into a single theory. They predict electromagnetic waves and form the foundation for modern technology including radio, television, and wireless communication. These equations represent one of the greatest achievements in theoretical physics.