Definition: According to this principal, total electric flux through a closed field enclosing a charge is 1/ε_o times the magnitude of the charge enclosed i.e. Φ = 1/ε_o(Q_enc)

Gaussian Surface: Gauss's law is valid for symmetrical charge distribution. Gauss's law is very effective in determining electric field in those cases where electric field is symmetrical around the source giving it. Electric field may be computed very easily by the clever choice of a closed surface that encloses the source charges. Such a surface is called "Gaussian surface". This surface could goes through the point where electric field is to be calculated and must have a shape according to the symmetry of source.

e.g. If suppose a charge Q is placed at the centre of a hemisphere, then to determine the flux through this body to enclose the first charge we will have to imagine a Gaussian surface. This imaginary Gaussian surface will be a hemisphere as shown.

Gauss's law is a powerful tool for determining electric field in case of symmetrical charge distribution by choosing a Gaussian surface in such a way that  is either parallel or perpendicular to it's various faces.

e.g. Electric field due to infinitely long line of charge: Let us consider a uniformly charged wire of infinite length having a constant linear charge density is . Let P be a point distant r from the wire at which the electric field is to be calculated.

Draw a cylinder (Gaussian surface) of radius r and length l around the line charge which encloses the charge Q (Q = l.l). Cylindrical Gaussian surface has three surfaces; two circular and one curved for surfaces (1) and (2) angle between electric field and normal to the surface is 90° i.e., q = 90°.

So flux linked with these surfaces will be zero. Hence net flux will goes through curved surface and it is

                                                . . . (i)

According to Gauss's law, Φ = Q/ε_o                             . . . (ii)

Equating equation (i) and (ii)

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