Electric Field Strength Due to Electric Excitation

Abstract

We start with the modified Maxwell equations without electric and magnetic charges, having constant scalars for the permeability µ and the permittivity ϵ. The following equations apply to a medium at rest: $$curlH = \in \frac{{\partial E}}{{\partial t}} + {{g}_{e}}$$ (1) $$- curlE = \mu \frac{{\partial H}}{{\partial t}} + {{g}_{m}}$$ (2) $$epsilon divE = \mu divH = 0$$ (3) $$\epsilon E = D,\mu H = B$$ (4) We restrict the investigation to currents that are carried either by electric or magnetic dipoles and avoid any monopole currents. This assumption will be ideally satisfied in a medium with atomic hydrogen, if any ionization can be neglected. For the electric dipole current density we use Eq.(1.2-11), writing the partial derivative ∂ge /∂t since the current density may now be a function of location as well as of time, $$\begin{array}{*{20}{c}} {{{g}_{e}} + {{\mathcal{T}}_{{mp}}}\frac{{\partial {{g}_{e}}}}{{\partial t}} + \frac{{{{\mathcal{T}}_{{mp}}}}}{{\mathcal{T}_{p}^{2}}}\int {{{g}_{e}}dt = {{\sigma }_{p}}E} } \\ {{{\sigma }_{p}} = \frac{{{{N}_{0}}{{e}^{2}}{{\mathcal{T}}_{{mp}}}}}{m}} \\ \end{array}$$ (5) but the use of Eqs.(1.3-26), (1.3-29), (1.3-31), and (1.3-32) for the magnetic dipole current density gm(t) runs into the difficulty of containing the function sin ϑ. There is little hope of finding an analytical solution of Maxwell’s modified equations (1)–(4) if the magnetic dipole current density gm is defined by a transcendental differential equation. We get around this difficulty by observing that the plots of Figs.1.3-3 and 1.3-5 for a hypothetical magnetic charge dipole are similar to the plots of Figs.1.3-11 and 1.3-10 for a bar magnet dipole.