# Governing Electromagnetics: Maxwell’s Equations

• Tarek I. Zohdi
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 64)

## Abstract

Some fundamental definitions and observations in conjunction with electromagnetic phenomena are:

• If a point charge q experiences a force $${\emph \bf{\Psi}}^e$$, the electric field, $${\emph \bf E}$$, at a position of the charge is defined by $${\emph \bf{\Psi}}^e=q {\emph \bf E}$$.

• If the charge is moving, another force may arise, $${\emph \bf{\Psi}}^m$$, which is proportional to its velocity $${\emph \bf{v}}$$. This other field is denoted as the “magnetic induction” (induced force field) or just the “magnetic field,” $${\emph \bf{B}}$$, such that $${\emph \bf{\Psi}}^m = {\it qv} \times{\emph \bf{B}}$$.

• If the forces occur concurrently (the charge is moving through the region possessing both electric and magnetic fields), then $${\emph \bf{\Psi}}^{em}=q{\emph \bf{E}} + {\it qv} \times{\emph \bf{B}}$$.

• Electric fields are produced by both electric charges and time-varying magnetic fields. Similarly, magnetic fields are induced by electric currents and by time-varying electric fields.

## Keywords

Point Charge Current Element Straight Wire Electric Flux Phenomenological Term
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.