Maxwell's equations

Electromagnetism
Electricity · Magnetism · Magnetic permeability
Electrostatics Electric charge • Coulomb's law • Electric field • Electric flux • Gauss's law • Electric potential energy • Electric potential • Electrostatic induction • Electric dipole moment • Polarization density
Magnetostatics Ampère's law • Electric current • Magnetic field • Magnetization • Magnetic flux • Biot–Savart law • Magnetic dipole moment • Gauss's law for magnetism
Electrodynamics Lorentz force law • emf • Electromagnetic induction • Faraday’s law • Lenz's law • Displacement current • Maxwell's equations • EM field • Electromagnetic radiation • Liénard–Wiechert potential • Maxwell tensor • Eddy current
Electrical Network Electrical conduction • Electrical resistance • Capacitance • Inductance • Impedance • Resonant cavities • Waveguides
Covariant formulation Electromagnetic tensor • EM Stress-energy tensor • Four-current • Electromagnetic four-potential
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Maxwell's equations describe how electric charges and electric currents create electric and magnetic fields. They describe how an electric field can generate a magnetic field.

In the 1860s James Clerk Maxwell published equations that describe how charged particles give rise to electric and magnetic force per unit charge. The force per unit charge is called a field. The particles could be stationary or moving. These, and the Lorentz force equation, give everything one needs to calculate the motion of classical particles in electric and magnetic fields.

The first equation allows one to calculate the electric field created by a charge. The second allows one to calculate the magnetic field. The other two describe how fields 'circulate' around their sources. Magnetic fields 'circulate' around electric currents and time varying electric fields: Ampère's law with Maxwell's extension, while electric fields 'circulate' around time varying magnetic fields: Faraday's law.