M. Fabbrichesi , SISSA

2. Maxwell's equations

In the first part of this lesson, Maxwell's equations are reminded to the students first by explaining their meaning and then by expressing them through mathematical symbols (integral forms are used). Meanings of flux and circuitation of a field are introduced through an analogy with water currents

and whirlpools. The minus sign appearing in the law ("lenz law") ∫ **E **d**ℓ**=-d/dt(∫ **B ****dS**) is associated to the energy conservation. It is then remarked that Gauss law is completely equivalent to Coulomb law for the force between two charges. Next, Gauss and Stokes theorems are reminded in order to write Maxwell's equations in differential form. While **E **field is generated by charges no monopole exists for the magnetic field i.e. ∇⋅ **B**=0. The latter is generated by currents **J **like Oersted first noticed. The second part begins with the continuity equation for the electric charge that leads to the concept of *local conservation*. Then follows a discussion on the *units *used in this course. The first set is the standard SI system, the second set is the given by the Gauss units (CGS). It is then mentioned the Ampere's law for the force between two wires.