Physics 114

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Electric flux, Gausss law
Carl Friedrich Gauss

• Physics 114

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Concepts

• Primary concepts
• Electric flux

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Laws

• Gausss law

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Definition of electric flux

• Flux means flow
• Nothing is actually flowing
• Other than that thinking of flow really helps to
  understand the flux

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Electric flux

• If electric field is rain electric flux is the
  amount of water in a bucket accumulated per unit
  of time
• Only component of the field perpendicular to the
  area A contributes to the flux

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Electric flux

• Alternatively we can define a vector A, which
  equals to the area A and is directed
  perpendicularly to the area

Flux is proportional to the number of field lines
going through the surface
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Compare fluxes
2
1

• Which flux is larger?
• 1). F1gtF2 2). F1ltF2 3). F1F2

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Compare fluxes
2
1

• Which flux is larger?
• 1). F1gtF2 2). F1ltF2 3). F1F2

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Compare fluxes
1
2

• Which flux is larger?
• 1). F1gtF2 2). F1ltF2 3). F1F2

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Compare fluxes
1
2

• Which flux is larger?
• 1). F1gtF2 2). F1ltF2 3). F1F2

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Compare fluxes
1
2

• Which flux is larger?
• 1). F1gtF2 2). F1ltF2 3). F1F2

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Compare fluxes
2
1

• Which flux is larger?
• 1). F1gtF2 2). F1ltF2 3). F1F2

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Non-uniform field, irregular surface

• Closed surface
• Influx lt0
• Outfluxgt0

Dont worry, well only deal with simple
surfaces Complex surfaces can be handled using
numeric integration by a computer.
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Why do we need flux?

• Gausss law

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Gauss? Coulomb

• Calculate E of point like () charge Q
• Consider sphere radius r centered at the charge
• Spherical symmetry E is the same everywhere on
  the sphere, perpendicular to the sphere

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Sinks and sources

• What goes in goes out
• unless
• there is a source (positive charge)
• or a sink (negative charge)

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Whats the flux?

• F1? F2?

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Respect the symmetry

• Find electric field for the following
  configurations
• Uniformly charged sphere. Charge Q, radius R.
• Long uniform line of charge. Charge per unit
  length l.
• Infinite plane of charge. Charge per unit of area
  s

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Field near conductor

• Infinite plane of charge. Charge per unit of area
  s
• Field inside conductor
• is zero, outside perpendicular
• to the surface.

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Two parallel plates

• Infinite plates
• One positive, one negative,
• Same charge density s

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