Practice question · Sort into groups

Sort each Maxwell equation by whether it involves divergence or curl.

Groups: Divergence (∇ $\cdot)$ · Curl (∇ $\times)$

$\nabla \cdot E$ = $\rho$ / $\varepsilon_{0}$
$\nabla \times B$ = $\mu_{0}J$ + $\mu_{0} \varepsilon_{0}$ $\partial E/\partial t$
Faraday's law
Gauss's law for E
$\nabla \times E$ = − $\partial B/\partial t$
$\nabla \cdot B$ = 0

Hints

Divergence appears in the flux laws, curl in the circulation laws.
Two fall into each category.

Show the answer

Divergence (∇ $\cdot)$ : $\nabla \cdot E$ = $\rho$ / $\varepsilon_{0}$ , $\nabla \cdot B$ = 0, Gauss's law for E

Curl (∇ $\times)$ : $\nabla \times E$ = − $\partial B/\partial t$ , $\nabla \times B$ = $\mu_{0}J$ + $\mu_{0} \varepsilon_{0}$ $\partial E/\partial t$ , Faraday's law

Why

Two equations use divergence (flux laws); two use curl (circulation laws).

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Sort each Maxwell equation by whether it involves divergence or curl.

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