Tag Info

The classical theory of electric and magnetic fields, both in the static and dynamic case. Also covers general questions about magnets, electric attraction/repulsion etc. Distinct from electrical-engineering.

When to Use this Tag

covers the classical description of both static and dynamic electromagnetic phenomena, summarised in Maxwell’s equations. For the discussion of electric circuitry, use instead, while should be used for the (non-classical) QFT approach to electromagnetism.

Relevant quantities

An electric charge is often denoted by $q$, an electric current by a vector field $\vec j$. They give rise to the electric field $\vec E$ and the magnetic field $\vec B$, which can be described as derivatives of the scalar electric potential $\phi$ and the vector potential $\vec A$. To reach an obviously Lorentz invariant formulation, these potentials are combined in the four-potential $A^\mu \equiv \left(\frac{1}{c} \phi , \vec A\right)^T$, which then allows us to define the electromagnetic field tensor $F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$.

Introduction

Maxwell’s equations provide a classical description of the phenomena arising from static and moving electric charges, such as the electron. The relevant quantities are the electric field $\vec E$ and the magnetic field $\vec B$, which obey Maxwell’s equations.

The distinction between static electromagnetism and electrodynamics is helpful in the beginning: In the static cases, charges $q$ effecting an electric field are assumed to be stationary and currents $\vec j$ causing a magnetic field do not change magnitude or direction. The dynamical case allows for both of these to happen, leading to electromagnetic waves and time-dependant magnetic and electric fields.