Gauss's law

In physics, Gauss's Law givesrelation betweenelectric flux flowing outclosed surface andcharge enclosed insurface:

where iselectric field, isarea ofdifferential square onsurface Aan outward facing surface normal defining its direction, ischarge enclosed bysurface, ispermittivityfree space isintegral oversurface A.

Incase ofspherical surface withcentral charge,electric fieldperpendicular tosurface, withsame magnitude at all pointsit, givingsimpler expresion:

where E iselectric field strength, Q isenclosed charge, A isarea ofsphere,ε₀ ispermittivityfree space.

Gauss's law can be useddemonstrate that thereno electric field insideFaraday cage without electric charges. Gauss's law iselectrical equivalentAmpere's law, which dealsmagnetism. Both equations were later integrated into Maxwell's equations.

It was formulated by Carl Friedrich Gauss1835, but was not published until 1867.