Gauss's Law

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Introduction

Gauss’s law is an expression of the general relationship between the net electric flux through a closed surface (Gaussian surface) and the charge enclosed by the surface. In order to understand this law one must first define and examine the term ‘flux’

Electric Flux

In general, ‘flux’ refers to the rate of flow per area, and so electric flux refers to the rate of flow of electric field lines through a given area. Thus electric flux is the product of the magnitude of the electric field and the surface area perpendicular to it, as given by the equation:

ΦE = EA

Where ΦE represents electric flux in Voltmeters (Vm) or ::Newton-metres-squared-per-coulomb (Nm2C-1)

E represents the electric field (NC-1)
A represents perpendicular area (m2)

Eflux.gif

  • The perpendicular area is given by the product of area and the cosine of the angle between the surface and the normal to the field lines. This means that flux is zero when the surface is parallel to the field lin (as Cos90° = 0)
  • For more complicated and non-uniform surfaces, the net flux is calculated as the sum of the fluxes through small areas of the surface ΔA. The method of summing these fluxes is called surface integration, and uses the slightly different integration symbol:
  • For a closed surface an electric field line leaving the surface causes positive flux, while field lines entering the surface cause negative flux
  • Thus the net flux is proportional to the total number of field lines leaving the object minus the total number of field lines entering the object
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