Lecture 1.2 - Electric Fields

ELEC2300

Electric Fields

An electric field is a vector field that shows the direction that a positively charged particle will move when placed in the field. More precisely, if a particle has an electric charge $q$ and is in an electric field $\vec{E}$, the electric force the charge will feel is $\vec{F}=q\cdot \vec{E}$. Electric fields are caused by electric charges, described by Gauss’s law, or varying magnetic fields, described by Faraday’s law of induction. The equations of both fields are coupled and together form Maxwell’s equations that describe both fields as a function of charges and currents.

Electrostatics

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In the special case of a steady state (stationary charges and currents), the Maxwell-Faraday inductive effect disappears. The resulting two equations (Gauss’s law $\nabla \times \mathbf{E}=\frac{p}{{ϵ}_0}$ and Faraday’s law with no induction term $\det \times \mathbf{E}=0$), taken together, are equivalent to Coulomb’s Law:

$${\mathbf{F}}_{01}=\frac{q_1{q}_0}{4\pi {ϵ}_0}\times \frac{{\hat{\mathbf{r}}}_{01}}{r_{01}^2}.$$