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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
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
gauss s law
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
example arbitrary hollow conductor
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!

example field of an infinitely long line charge
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
slide5
Three surfaces
    • Top, bottom, & side
  • Net flux
  • Charge enclosed
slide7
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?