Electrostatics

This chapter provides an overview of electrostatics. Electrostatics in its most restrictive sense is the specialization of Maxwell's equations to a system whose sources are steady-state, time-invariant electric charges. Because the conservation of charge is implicit in this definition, the unifying principle of all the equations is the conservation of total electric flux. Therefore, electrostatics also properly includes steady-state conduction current problems. In this chapter the fundamental relationship between source and field is between the electric charge q and the electric flux density D because that relationship has the form of a conservation law. The electric field E is introduced with the concept of the electrostatic potential Φ as the quantity involved in the dynamics of electrostatic systems (i.e., their interaction forces and energies). In this way,ɛ (measured in farads per meter), the permittivity of the material medium through which the flux traverses, appears as a proportionality constant that gauges the amount of energy stored in a given electrostatic system. Capacitance C (measured in farads) is then a purely geometric expression of the arrangement of that energy inside the system. The concepts of electrostatics are extended to the case of current flow in resistive environments by the recognition of the formal analogy between the electrostatic flux and the current density flux j. Wherever possible, the method of derivation of the important results is indicated.