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(1.33)

This shows that the divergence of the magnetic field (∇ • B) is always zero, which means that the magnetic field lines are closed loops, thus the integral of B over a closed surface is zero.

For a time‐harmonic EM field (which means the field linked to the time by factor e^jωt where ω is the angular frequency and t is the time), we can use the constitutive relations

(1.34)

to write Maxwell’s equations into the following forms

(1.35)

where B and D are replaced by the electric field E and magnetic field H to simplify the equations and they will not appear again unless necessary.

It should be pointed out that, in Equation (1.35), can be viewed as a complex permittivity defined by Equation (1.20). In this case, the loss tangent is

(1.36)

It is hard to predict how the loss tangent changes with the frequency since both the permittivity and conductivity are functions of frequency as well. More discussion will be given in Chapter 3.