As long as Maxwell equations are linear, then the so-called principle of superposition holds. This means that any linear combination of two or more solutions still represents a solution of the same equations subject to the same boundary conditions. We have already implicitly exploited this principle in many situations, e.g., for the definition of time-harmonic fields and the construction of the Dirichlet Green function. What is more, all the integral representations for fields and potentials discussed in previous chapters were derived by exploiting the linearity of Maxwell's equations and the principle of superposition. In this regard, we may even interpret an integral involving sources and a suitable Green function as the linear combination of infinitely many elementary solutions.

Chapter Contents:

• 6.1 Principle of superposition
• 6.2 Well-posedness of the Maxwell equations
• 6.3 Uniqueness in the time domain
• 6.3.1 Bounded regions
• 6.3.2 Unbounded regions
• 6.4 Uniqueness in the frequency domain
• 6.4.1 Bounded regions
• 6.4.2 Unbounded regions
• 6.5 Magnetic charges and currents
• 6.6 Boundary conditions with magnetic sources
• 6.7 Duality transformations
• 6.8 Reciprocity theorems
• 6.8.1 Frequency domain
• 6.8.2 Non-reciprocal media
• 6.8.3 Time domain
• 6.9 Other symmetry relationships
• 6.9.1 Electrostatic fields
• 6.9.2 Stationary fields and steady currents
• References

Inspec keywords: Maxwell equations; Green's function methods

Other keywords: Dirichlet Green function; electromagnetic field properties; Maxwell equations; time-harmonic fields

Subjects: Electromagnetic waves: theory; Function theory, analysis; Electromagnetic wave propagation; Mathematical analysis