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Week 3 Week 3 –– Chapter XXIVChapter XXIV

�� Coulomb’s LawCoulomb’s Law�� Flux of an Electric FieldFlux of an Electric Field�� Gauss’ LawGauss’ Law

–– A Charged Isolated ConductorA Charged Isolated Conductor

–– Cylindrical SymmetryCylindrical Symmetry

–– Planar SymmetryPlanar Symmetry

–– Spherical SymmetrySpherical Symmetry�� Homework: Chapter XXIV Homework: Chapter XXIV –– 5E, 18P, 29P 5E, 18P, 29P

Coulomb’s Law and FluxCoulomb’s Law and Flux

Gauss’ law relates the electric fields at a point Gauss’ law relates the electric fields at a point on a (closed) on a (closed) Gaussian Gaussian surface and the net surface and the net charge enclosed by that surface.charge enclosed by that surface.

Gauss’ law uses symmetry Gauss’ law uses symmetry and is fully equivalent to and is fully equivalent to Coulomb’s law. Coulomb’s law.

Which one you have to use Which one you have to use depends on the application!depends on the application!

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Flux of an Electrical FieldFlux of an Electrical Field

Electric flux through Electric flux through a a Gaussian Gaussian surfacesurface

((discrete form)discrete form)

(integral form)(integral form)

The electric flux The electric flux ΦΦ through a through a Gaussian Gaussian surface is proportional surface is proportional to the number of f ield lines to the number of f ield lines passing through that surface.passing through that surface.

Sample Problems XXIV Sample Problems XXIV –– 1 and 21 and 2

A A Gaussian Gaussian surface in the surface in the form of a cylinder of radius form of a cylinder of radius RR is immersed in a uniform is immersed in a uniform electric field electric field EE, with the , with the cylinder axis parallel to the cylinder axis parallel to the field. What is the fluxfield. What is the flux ΦΦ of of the electric field through the electric field through this closed surface?this closed surface?

A A nonuniform nonuniform electric field electric field is given by is given by EE = 3= 3xxii + 4+ 4jjpierces the cube. What is pierces the cube. What is the electric flux through the the electric flux through the right face, the left face, and right face, the left face, and the top face?the top face?

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Gauss’ LawGauss’ Law

Gauss’ lawGauss’ law

Gauss’ lawGauss’ law

Gauss’ law and Coulomb’s lawGauss’ law and Coulomb’s law

A Charged Isolated ConductorA Charged Isolated ConductorIf an excess charge is If an excess charge is placed on an isolated placed on an isolated conductor, the amount conductor, the amount of charge wil l move of charge wil l move entirely to the surface entirely to the surface of the conductor. None of the conductor. None of the excess charge of the excess charge will be found within the will be found within the body of the conductor.body of the conductor.

Conducting Conducting surfacesurface

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Cylindrical and Planar SymmetryCylindrical and Planar Symmetry

Planar symmetryPlanar symmetryCylindrical symmetryCylindrical symmetry

Sample Problems XXIV Sample Problems XXIV –– 3 and 43 and 4

Five charged lumps of plastic and Five charged lumps of plastic and an electrically neutral coin are an electrically neutral coin are shown. The cross section of a shown. The cross section of a Gaussian Gaussian surface surface SS is indicated. is indicated. What is the net flux through the What is the net flux through the surface if surface if qq11 = = qq44 = + 3.1 = + 3.1 nCnC, , qq22 = = qq55 = = −−5.9 5.9 nCnC, and , and qq33 = = −− 3.1 3.1 nCnC??

A cross section of a spherical metal A cross section of a spherical metal shell of inner radius shell of inner radius RR is shown. A is shown. A point charge of point charge of −−5.0 5.0 µµC is located at a C is located at a distance distance RR/2 from the center of the /2 from the center of the shell . If the shell i s electrically neutral, shell . If the shell i s electrically neutral, what are the (induced) charges on its what are the (induced) charges on its inner and outer surfaces? What is the inner and outer surfaces? What is the field inside and outside the shell?field inside and outside the shell?

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Spherical SymmetrySpherical Symmetry

Spherical shellSpherical shell

Uniform charge Uniform charge (field at (field at rr ≤≤ RR))

A shell of uniform charge attracts or repels a A shell of uniform charge attracts or repels a charged particle that is outside the shell as if charged particle that is outside the shell as if the shell ’s charge were concentrated at the the shell ’s charge were concentrated at the center of the shell .center of the shell .

A shell of uniform charge exerts no A shell of uniform charge exerts no electrostatic force on a charged particle that electrostatic force on a charged particle that is located inside the shell.is located inside the shell.

Sample Problem XXIV Sample Problem XXIV –– 66

Portions of two large, parallel, Portions of two large, parallel, nonnon--conducting sheets, each with a conducting sheets, each with a fixed uniform charge on one side fixed uniform charge on one side are shown. The magnitudes of the are shown. The magnitudes of the surface charge densities are surface charge densities are σσ(+)(+) = 6.8 = 6.8 µµC/mC/m22 for the positively for the positively charged sheet and charged sheet and σσ((−−)) = 4.3 = 4.3 µµC/mC/m22

for the negatively charged sheet. for the negatively charged sheet. Find the electric field Find the electric field EE (a) to the (a) to the left of the sheets, (b) between the left of the sheets, (b) between the sheets, and (c) to the right of the sheets, and (c) to the right of the sheets. sheets.