Course notes

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MAXWELL EQUATIONS 1.1 Introduction In this chapter we introduce the equations, already discussed in other courses, that are at the basis of the propagation of the electromagnetic waves which is the main issue we are interested in, and we analyse their basic properties. These equations ar e the starting point of the course because the electromagnetic waves are the mean through which we can transfer any information from one point to another one. In particular, we begin by recalling the relationships that are valid for the static fields (electrostatic and magnetostatic fields) a nd in succession we analyse how they modify in order to take into account the variation in time of the different vector fiel ds. We derive the wave solution in the particular case when the field generators are set to infinity and we studying detail the properties of this particular solution. Finally, we move the source of the electromagnetic field within the space where the electromagnetic field is analysed, situation that mimic the electromagnetic wave generated by an antenna. 1.2 Static fields The vector quantities that are peculiar of the elect rostatic and magnetostatic fields are the electric field vector E and the magnetic field vector B, respectively. They are related to their generators that are the electric charge density and the current density in the following way: (1.1) 0= × ∇E ρ= ⋅ ∇D (1.2) (1.3) J H= × ∇ 0= ⋅ ∇B (1.4) Each one of considered quantities depends on the position: E(x,y,z) [V/m] is the electric field vector, D(x,y,z) [ C/m2] is the electric flux density also known as the displacement vector or the electric induction, H(x,y,z) [A/m] is the magn etic field intensity and B(x,y,z) [Wb/m2] is the magnetic flux density or magnetic induction. The relationships reported above…