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The Maxwell Equations

One the the most important applications of the concepts you have learned are the equations which describe classical electricity and magnetism. When we set as the electric field,   as the magnetic field, as the electric displacement field, and as the magnetizing field, then the equations describing these quantities are

We can integrate all these equations to get the integral forms:

The four laws are called, respectively, Coulombs/Gauss' Law, absence of magnetic monopoles, Faraday's/Induction Law, and Ampère's Law. Together, they are called the Maxwell equations, after James Clerk Maxwell.