Chapter 7 - Electrodynamics

Reference "Introduction to Electrodynamics" (5e) by David Griffiths.

Electrostatics is the study of the electric field $\vec{E}$ of static electric charges; magnetostatics is the study of the magnetic field $\vec{B}$ of moving electric charges. Electrodynamics is therefore the study of the electric field $\vec{E}$ of moving electric charges.

Electromotive Force

To make a current flow, some force on the charges is needed - thus, current density can be written as proportional to the force per unit charge $\vec{f}$. $$\vec{J}=\sigma \vec{f}=\sigma (\vec{E}+\vec{v}\times \vec{B})$$

Usually, the charge velocity is small enough that $\vec{v}\times \vec{B}=0$, so we can represent it as $$\vec{J}=\sigma \vec{E}\text{(weird-lookin’ Ohm’s law)}$$ This works because $\vec{E}\ne 0$ for moving charges within a conductor, though $\vec{E}=0$ for static.

To convert current density to current: $$I=\int \vec{J}\cdot d\vec{a}$$

$\sigma$ is the conductivity of a material, with the resistivity being $$\rho =\frac{1}{\sigma }$$

• Metals can be regarded as perfect conductors: $\sigma \approx \infty$
• Insulators/dielectrics: $\sigma \approx 0$

Resistors are made of low-conducting (hence high-resistivity) materials.