Spherical Symmetry

Gaussian Surface: Concentric Sphere

Gaussian Symmetry

Choose the charge symmetry, then match it with a Gaussian surface where \(E\) is constant or the flux is zero on each part.

Symmetry

Current Match

Surface: concentric sphere around a point charge.

\(\Phi_E=E(4\pi r^2)=\dfrac{Q_{\mathrm{enc}}}{\varepsilon_0}\)

The field has the same magnitude everywhere on a concentric sphere.

Charge source
Gaussian surface
Electric field