GITAM, Department of Engineering Physics
Gauss's Law
The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.
The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field. Gauss's Law is a general law applying to any closed surface. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.
Gauss' Law, Integral Form
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The area integral of the electric field over any closed surface is equal to the net charge enclosed in the surface divided by the permittivity of space. |
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Gauss' law permits the evaluation of the electric field in many practical situations by forming a symmetric Gaussian surface surrounding a charge distribution and evaluating the electric flux through that surface.