Encyclopedia > Gauss's law

  Article Content

Gauss's law

In physics, Gauss's Law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface:

<math>\oint_A \mathbf{E} \cdot d\mathbf{A} = \frac{Q_\mbox{A}}{\epsilon_0}</math>

where <math>\mathbf{E}</math> is the electric field, <math>d\mathbf{A}</math> is the area of a differential square on the surface A with an outward facing surface normal defining its direction, <math>Q_\mbox{A}</math> is the charge enclosed by the surface, <math>\epsilon_0</math> is the permittivity of free space and <math>\oint_A</math> is the integral over the surface A.

In the case of a spherical surface with a central charge, the electric field is perpendicular to the surface, with the same magnitude at all points of it, giving the simpler expresion:

<math>E={Q \over \epsilon_0 A}</math>

where E is the electric field strength, Q is the enclosed charge, A is the area of the sphere, and ε0 is the permittivity of free space.

Gauss's law can be used to demonstrate that there is no electric field inside a Faraday cage without electric charges. Gauss's law is the electrical equivalent of Ampere's law, which deals with magnetism. Both equations were later integrated into Maxwell's equations.

It was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
242

... 2nd century - 3rd century - 4th century Decades: 190s 200s 210s 220s 230s - 240s - 250s 260s 270s 280s 290s Years: 237 238 239 240 241 - 242 - 243 244 245 246 ...

 
 
 
This page was created in 25.4 ms