Tag Info

Electrostatics is concerned with the electrical fields and scalar potentials of stationary electrical charges and charge distributions. Use this for questions about electromagnetic situations in which currents and magnetic fields are absent, otherwise use the [electromagnetism] and/or [magnetic-fields] tags.

When to Use this Tag

covers the classical description of static electromagnetic phenomena, summarised in Maxwell's equations. It is a subfield of that addresses the static case, that is, those situations where the fields and sources are independent of time.

Under the static assumptions, the formalism becomes unable to describe dynamical phenomena, such as electromagnetic waves. Moreover, if the fields are time-independent, the electric and magnetic fields decouple and can be described independently from one another. For this reason, is typically used to when discussing electric fields alone, while is used when one is interested in magnetic fields.

The basic equations

In the static approximation, Maxwell's equation are simplified into $$\nabla\cdot\vec E=4\pi\rho,\qquad \nabla\times\vec B=\frac{4\pi}{c}\vec j$$$$\nabla\cdot\vec B=\nabla\times\vec E=0$$

These equations, together with some appropriate boundary conditions, determine the value of the electric and magnetic fields uniquely. For example, in the case of a stationary point charge at the origin, one finds $$\vec E=-\frac{q}{r^3}\vec r$$

Finally, the equations $\nabla\cdot\vec B=\nabla\times\vec E=0$ imply that we may write $\vec E$ and $\vec B$ in terms of the derivatives of the so-called scalar and vector potentials, $$\vec E=-\nabla\phi,\qquad \vec B=\nabla\times\vec A$$

See for more details.