Set of four equations that describe the behavior of electric and magnetic fields, including Gauss's law, Ampere's law, Faraday's law, and the magnetic equivalent of Gauss's law.
Vector calculus: :.
Gauss's Law: :.
Ampere's Law: :.
Gauss's Law for electric field: This equation describes how the electric field emanates from electric charges. It states that the total electric flux through any closed surface is proportional to the electric charge enclosed within the surface.
Gauss's Law for magnetic field: This equation describes how the magnetic field is generated by magnetic charges. It states that there are no magnetic charges in the universe, and therefore the total magnetic flux through any closed surface is always zero.
Faraday's Law of electromagnetic induction: This equation explains how a changing magnetic field can create an electric field. It states that the electromotive force (EMF) induced in any closed loop is proportional to the time variation of the magnetic flux through the loop.
Ampere's Law with Maxwell's modification: This equation explains how a changing electric field can create a magnetic field. It states that the circulation of magnetic field around any closed loop is proportional to the sum of the currents passing through the loop and the time variation of the electric flux through the loop.
The wave equation: This equation describes the propagation of electromagnetic waves in free space. It is derived by combining the four original Maxwell equations and assuming that the electric and magnetic fields vary sinusoidally with time and space.
The Lorentz force equation: This equation describes the force experienced by a charged particle moving in an electromagnetic field. It states that the force is proportional to the electric field and the velocity of the particle, and to the magnetic field and the velocity of the particle.
The continuity equation: This equation describes the conservation of charge in a given volume. It states that the rate of change of charge in a volume is equal to the net current flow into or out of the volume.
The Poynting vector equation: This equation describes the direction and intensity of electromagnetic energy flow. It states that the electromagnetic energy flux density (the Poynting vector) is proportional to the cross product of the electric and magnetic fields.