Flux through a closed region

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Flux through a closed region - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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

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
• Let l be charge per unit length
• Symmetries
• Axis translation (z-axis)