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Lect02 - Electric Flux Electric Potential Physics 104...

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Electric Potential Gauss Law (continued from Chapter 17) Chapter18: Electric potential energy Electric potential: Voltage Equipotential and field lines, conductors Physics 104, Lecture 2 Sep 12, 2011 Electric Flux To define Gauss’ Law, a quantity called electric flux is needed The electric flux is equal to the number of electric field lines that pass through a particular surface multiplied by the area of the surface. Electric flux Φ E = EA cos θ Electric Flux – closed surfaces Flux through close surfaces: Positive when outgoing, negative for ingoing Consider case when no charge is inside: An equal number of lines going in and out (field lines can only start or end in a charge!) net flux is zero! Need a charge inside for a net flux through closed surface: This brings us to Gauss Law ... Gauss’ Law The electric flux through any closed surface is proportional to the charge q inside the surface The constant ε o is the emissivity of free space This was encountered in one form of Coulomb’s Law Since the flux depends on the electric field, Gauss’ Law can be used to find the field! Section 17.5 Φ E = q ε o Karl Friedrich Gauss 1777-1855 Considered one of the most influential mathematicians and scientists Gauss’ Law: Point Charge Choose a Gaussian surface Want a surface that will make the calculation as easy as possible Choose a surface that matches the symmetry of the problem For a point charge, the field lines have a spherical symmetry Electric Flux: Gauss Law: Electric field at distance r easily obtained from Gauss Law Section 17.5 Φ E = EA Sphere = 4 π r 2 E Φ E = q ε o E = q 4 πε o r 2 Gauss’ Law: Determine Electric Field from Line of Charge The line of charge has a total length h and a total charge Q The electric field is perpendicular to the line Choose a cylinder of radius r for the Gaussian surface: E = Q 2 πε o hr Section 17.5 Φ E = q ε o Φ E = EA cyl = E 2 π rh Flux Gauss El. field follows: A = 2 π rh

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Lect02 - Electric Flux Electric Potential Physics 104...

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