Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 22 Gauss’s Law

Copyright © 2012 Pearson Education Inc. Goals for Chapter 22 To use the electric field at a surface to determine the charge within the surface To learn the meaning of electric flux and how to calculate it To learn the relationship between the electric flux through a surface and the charge within the surface To use Gauss’s law to calculate electric fields To learn where the charge on a conductor is located

Copyright © 2012 Pearson Education Inc. Charge and electric flux Positive charge within the box produces outward electric flux through the surface of the box, and negative charge produces inward flux.

Copyright © 2012 Pearson Education Inc. Zero net charge inside a box Zero net charge inside a box and no net electric flux through the surface of the box.

Copyright © 2012 Pearson Education Inc. What affects the flux through a box? Doubling the charge within the box doubles the flux, but doubling the size of the box does not change the flux.

Copyright © 2012 Pearson Education Inc. Calculating electric flux For uniform electric field For nonuniform electric field

Copyright © 2012 Pearson Education Inc. Electric flux through a disk

Copyright © 2012 Pearson Education Inc. Electric flux through a cube

Copyright © 2012 Pearson Education Inc. Electric flux through a sphere Ex 22.3: Find the electric flux through the sphere. q = 3 μC, r = 0.2 m. Note: the electric flux is independent of the sphere size Gauss’s Law

Copyright © 2012 Pearson Education Inc. Point charge centered in a spherical surface The flux through the sphere is independent of the size of the sphere and depends only on the charge inside.

Copyright © 2012 Pearson Education Inc. Point charge inside a nonspherical surface The flux is independent of the surface and depends only on the charge inside.

Copyright © 2012 Pearson Education Inc. Positive and negative flux The flux is positive if the enclosed charge is positive, and negative if the charge is negative.

Copyright © 2012 Pearson Education Inc. General form of Gauss’s law What is the electric flux at service areas A, B, C, D?

Copyright © 2012 Pearson Education Inc. Applications of Gauss’s law Under electrostatic conditions, any excess charge on a conductor resides entirely on its surface. Example 22.5: Find the electric field of charged sphere at distance r.

Copyright © 2012 Pearson Education Inc. Field of a line charge Example 22.6: Find the electric field of an infinite long uniform line charge.

Copyright © 2012 Pearson Education Inc. Field of a sheet of charge Example 22.7: Find the electric field of an infinite plane sheet of charge.

Copyright © 2012 Pearson Education Inc. Field between two parallel conducting plates Example 22.8: Find the electric field between oppositely charged parallel conducting plates.

Copyright © 2012 Pearson Education Inc. A uniformly charged sphere Example 22.9: Find the electric field both inside and outside a sphere uniformly filled with charge. Follow Example for the charge on a hollow sphere.

Copyright © 2012 Pearson Education Inc. Charges on conductors Charges in a conductor having a cavity within it.

Copyright © 2012 Pearson Education Inc. A conductor with a cavity A solid conductor with a cavity carries a total charge of +7 nC. Within the cavity, insulated from the conductor, is a point charge of -5 nC. How much charge is on each surface (inner and outer) of the conductor?

Copyright © 2012 Pearson Education Inc. Testing Gauss’s law experimentally Follow the discussion of Faraday’s icepail experiment, which confirmed the validity of Gauss’s law. Use Figure below.

Copyright © 2012 Pearson Education Inc. The Van de Graaff generator The Van de Graaff generator, shown in Figure below, operates on the same principle as in Faraday’s icepail experiment.

Copyright © 2012 Pearson Education Inc. Electrostatic shielding A conducting box (a Faraday cage) in an electric field shields the interior from the field. (See Figure below.)

Copyright © 2012 Pearson Education Inc. Field at the surface of a conductor The electric field at the surface of any conductor is always perpendicular to the surface and has magnitude  /  0. Follow the discussion in the text, using Figure at the right. Follow Conceptual Example Follow Example 22.13, which deals with the electric field of the earth.