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In this chapter Maxwell’s equations are described and common ways to solve them analytically are discussed. The equations imply certain properties of matter with which it interacts and full solutions that describes this behavior analytically are provided from first principles. The chapter shows specifically that one can derive very fundamental properties with simple calculations. Furthermore, the concept of inductance and capacitance are highlighted by reference to their duality. Various high-speed phenomena are studied in some detail with particular attention to the current distributions induced by the magnetic field.
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