Electromagnetic Fields, Energy, and Forces

associated Cartesian chapter charge density charge distribution closed path coil conductor constant contour coordinates corresponding current density current distribution current filament current flowing defined derivative differential direction discussed in Sec distance E₁ electric charges electric field electromagnetic field electron equal to zero equipotential evaluated expressed field produced finite first-order flux four-vector frame function given by Eq grad help of Eq illustrated in Fig Laplace's equation Let us consider line integral linear macroscopic field magnetic charges magnetic dipoles magnetic field magnetized matter magnitude material Maxwell's equations obtained parallel plane plates polarization positive charge Poynting's theorem Poynting's vector Problem quantities represents resulting right-hand side satisfy scalar potential side of Eq solution of Laplace's spherical surface charge surface current surface integral tangent tensor terminal voltages theorem tion uniform unit vector vanish vector potential velocity volume wire yields z-axis μο