Electrical Engineering ⇒ Topic : Gausss Theorem

Gauss's Theorem

This theorem was first expressed by a German scientist Karl Fredrich Gauss (1777-1855) and may be stated as under

The electric flux passing through a closed surface surrounding a number of charges is equal to the algebraic sum of the charges inside the closed surface.

                                                         FIGURE (A)

To illustrate Gauss's theorem, consider Fig. 5.18 where charges Q₁,Q₂, Q₃ and Q₄ coulombs are placed inside a closed surface. According to Gauss, the total electric flux (Ψ) passing through this closed surface i.e

                                                Ψ =  the algebraic sum of the charges inside the closed surface i. e.

                                                    = (Q₁) + (Q₂) + (Q₃) + (-Q₄) Fig. 5.18

                                                    =  Q₁ + Q₂ + Q₃ - Q₄ coulombs

The following points may be noted :

• The location of charge/charges inside the closed surface does not matter.
• The shape of the surface does not matter provided it is a closed surface enclosing the charge/charges.