Flux and Gauss' Law

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Flux and Gauss' Law

• Ch 22
• AP Physics C

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Background

• Gauss Law is part of the key to using symmetry
  considerations to simplify E-Field calculations
  (remember section 21.5 when we integrated to
  solve for E of a ring of charge, line of charge
  etc.)
• In chapter 21 we asked
• What is the E-field due to a known charge
  distribution?
• In chapter 22 we will ask
• What is the charge distribution if we know E?

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The box may enclose a charge, by placing a test
charge and observing F, we know E. It is only
necessary to do this at the surface of the shape.
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Flux

• Flux, in this case Electric Flux, is the amount
  of (electric) field passing through a specified
  area.
• Think of water flowing in a pipe (flux comes from
  the Latin for flow)

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Pictures of outward () flux and inward (-) flux
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Situations where the total flux equals zero
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The E-field decreases at 1/r2 while the area
increases at r2 and that increase and decrease
cancel each other out and that is why the size of
the surface enclosing Q does not matter.
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Flux

• Symbol ??E
• Unit ? Nm2/C
• Equation

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What we can conclude about ?

• ? is proportional to q
• Whether ? is inward or outward depends on the q
  inside the surface
• A q outside the surface offers zero ? because ?in
  ?out

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? 0 through triangular prism below. See board
for the proof
E 500 N/C
50 cm
30 cm
40 cm
40 cm
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Gauss Law

• The total electric flux through any closed
  surface is proportional to the net electric
  charge inside the surface

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Gauss Law
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Point Charge
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Uniformly charge insulator at a varying r
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Line of Charge
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Sheet of Charge