# REVIEW SUMMARY Gauss Law

REVIEW SUMMARY Gauss Law

Gauss’ Law

Gauss’ law and Coulomb’s law although expressed in different forms are equivalent ways of describing the relation between charge and electric field in static situations Gauss’ law is

in which is the net charge inside an imaginary closed surface (a Gaussian surface) and  is the net Hux of the electric field through the surface

Coulomb’s law can readily be derived from Gauss’ law.

Applications of Gauss’ Law

Using Ga~ss’ law and, in some cases symmetry arguments, we can derive  Several important results in electrostatic situations Among these are 1. An excess charge on a conductor is located entirely on the outer surface of the conductor  The external electric field near the surface of a charged conductor is perpendicular to the surface and has magnitude

Within the conductor E = O 3. The electric field at any point due to ‘an infinite line of charge with uniform linear charge density’s perpendicular to the lineof charge and has magnitude

where r is the perpendicular distance from the line of charge’ to the point The electric field due to an infinitive nonconducting sheet with uniform surface charge denser Y (T is perpendicular to the plane of the sheet and has magnitude

The electric field outside asp helical shell of charge with radius R and total charge q is directed radially and has magnitude

Here r is the distance from 1 he center of the shell to the point at which E is measured. (The charge behaves for external points as if it were all local ed at the center of the sphere.) The field inside a uniform sphere cal shell of charge is exactly zero:  = 0 aerial shell for 6 The electric field inside inform sphere of charge is directed radially and has magnitude