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Flux through a closed region

Flux through a closed region. The net flux is proportional to the strength of the associated charge enclosed within a volume. F net = F out – F in Outflowing charge called source, inflowing charge called sink Flux measured through surfaces enclosing volume. Gauss’s Law.

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Flux through a closed region

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  1. Flux through a closed region • The net flux is proportional to the strength of the associated charge enclosed within a volume • Fnet = Fout – Fin • Outflowing charge called source, inflowing charge called sink • Flux measured through surfaces enclosing volume

  2. Gauss’s Law • Use definition of flux to connect to field strength • Replace real surface by an imaginary one • Gaussian surface • Electric permitivity of vacuum, e0 = 8.95 x 10-12 C2/N-m2 • Useful when symmetry can be used to determine direction by inspection • Reduces problem to counting strength of source and calculating surface area

  3. Example: Arbitrary hollow conductor What is the electric field inside an arbitrarily shaped conductor with a surface area of 10.0 m2 and a total surface charge of 45.0 C? No enclosed charge, so by Gauss’s Law, field is 0!

  4. Example: Field of an infinitely long line charge • Let l be charge per unit length • Symmetries • Axis translation (z-axis) • Rotation about axis • Field must be independent of z direction, and same around circle • Cylinder has same symmetries

  5. Three surfaces • Top, bottom, & side • Net flux • Charge enclosed

  6. By Gauss’s Law

  7. Symmetries: • Translational in plane • Rotational about center of plane • Cylinder through plane has these symmetries A rectangular sheet is 50.0 km by 250.0 km. It has a total charge of 300.0 MC. What is the electric field 10.0 m above the center of the sheet?

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