Electric Flux

1
Electric Flux

• PHYS 2326-5

2
Flux

• Electric field lines are tangent to the electric
  field vector at each point along the line
• Lines/unit area are proportional to the electric
  field
• For a uniform electric field perpendicular to a
  rectangular surface, FE the electric flux is FE
  EA (Nm2/C)
• Flux is proportional to the number of electric
  field lines penetrating a surface

3
Non Perpendicular Surface

• Taking a square that is not perpendicular to the
  surface, the relationship becomes
• FE EAcos? (Nm2/C)
• where ? is the angle between the surfaces
  (normals to the surfaces)

4
General Case
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Observations

• Closed surface one that totally surrounds a
  region
• The net number of lines means the total leaving
  the surface minus the total entering the surface
• If more leave than enter net flux is positive
• If less net flux is negative

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General Equation
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Example 1Cube in Uniform E field

• Fig. 24.5 E is in x direction, surfaces are l
  x l and the cube is oriented along the axes
• 2 Surfaces perpendicular to x-axis have flux E
  l2, The 4 surfaces parallel to the x-axis are
  oriented so that cos ? 0
• Note that one nonzero surface has E going in
  while the other is E going out, Net flux 0

8
Example 2

• Uniform electric field E 100N/C along the x
  axis through a cylinder of length 1m, radius 0.2m
  with A2 at x0 and A1 at x1m.
• What is flux through each surface and what is
  total flux

Y
A3
A2
X
Z
A1
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Equations

• A1A2 pr2
• A3 2pr