Kinetic Analysis and Characterization of Epoxy Resins ... - FedOA

Introduction 33
that describe the properties of the electric and magnetic fields and relate them to
their sources, charge and current density. According to these equations light is an
electromagnetic wave.
The equations are given in SI units, as matter of fact Maxwell’s equations are
not unchanged in other unit systems.
The following set of equations expresses the differential form of Maxwell’s laws in
terms of free charge and current:
∇ · D ⃗ = ρf Gauss’law
∇ · ⃗ B = 0 Gauss’law for magnetism
∇ × E ⃗ = − ∂ B ⃗
∂t
∇ × H ⃗ = J ⃗ f + ∂ D ⃗
∂t
Faraday’s law of induction
Ampère’s circuital law
(1.2)
While the integral form is expressed by the following set of equations:
∮
⃗ S
D · dA ⃗ = Q f,S Gauss’law
∮
⃗ S
B · dA ⃗ = 0 Gauss’law for magnetism
∮∂S
E ⃗ · d ⃗ l = − ∂Φ B,S
∂t
Faraday’s law of induction
∮∂S
H ⃗ · d ⃗ l = I f,S + ∂Φ D,S
∂t
Ampère’s circuital law
(1.3)
where the symbols used in the equations 1.2 and 1.3 are explained in the Table
1.2
Maxwell’s equations are generally applied to macroscopic averages of the fields,
which vary wildly on a microscopic scale in the vicinity of individual atoms 8 .Itis
only in this averaged sense that one can define quantities such as the permittivity
and permeability of a material.
At the microscopic level, Maxwell’s equations,
ignoring quantum effects, describe fields, charges and currents in free space, but
at this level of detail one must include all charges, even those at an atomic level,
generally it is an intractable problem.
8 Where they undergo quantum mechanical effects as well.
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