Maxwell’s Equations
The problem of electromagnetic analysis on a macroscopic level is that of solving Maxwell’s equations subject to certain boundary conditions. Maxwell’s equations are a set of equations, written in differential or integral form, stating the relationships between the fundamental electromagnetic quantities. These quantities are:
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Electric field intensity E
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Electric displacement or electric flux density D
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Magnetic field intensity H
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Magnetic flux density B
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Current density J
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Electric charge density ρ
The equations can be formulated in differential form or integral form. The differential form is presented here because it leads to differential equations that the finite element method can handle. For general time-varying fields, Maxwell’s equations can be written as:
The first two equations are also referred to as Maxwell–Ampère’s law and Faraday’s law, respectively. Equation three and four are two forms of Gauss’ law: the electric and magnetic form, respectively.
Another fundamental equation is the equation of continuity
Out of the five equations mentioned, only three are independent. The first two combined with either the electric form of Gauss’ law or the equation of continuity form such an independent system.