# Unit 1 Day 10 Electric Flux & Gauss’s Law

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Unit 1 Day 10 Electric Flux & Gauss’s Law
Definition of Electric Flux Electric Flux thru a Closed Surface Gauss’s Law Derivation of Gauss’s Law from Coulomb’s Law

Karl Friedrich Gauss 1777-1855 Developed a generalized and
more elegant relationship between charge and the electric field (Coulomb’s Law)

Electric Flux The electric flux refers to the electric field lines that penetrate a given surface For a given uniform electric field E passing thru an area A, the electric flux is defined as:

Electric Flux θ is the angle between the E-Field and the line drawn normal to the surface The electric flux thru an area is proportional to the number of E-Field Lines passing thru the area

Electric Flux Thru a Closed Surface
In general, an electric field is not uniform and the area is not flat ! Any area can be divided up into n number of small elements of surface area ΔA, sufficiently small to be considered flat and the E-field is rather invariant over this small area. Then:

Electric Flux Thru a Closed Surface
In the limit as the sum becomes an integral Then a surface of any shape that completely encloses a volume of space is given by

Electric Flux Thru a Closed Surface
A (+) flux leaving the volume A (-) flux entering the volume If every field line that enters a volume exits the volume, then: ; there is no net flux into or out of the closed surface The net flux will be non-zero only if the surface encloses a net charge The value of depends on the charge enclosed by the surface. This is Gauss’s Law !

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