Physics 212 lecture 4: Electric Flux and Gausss Law

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Physics 212 lecture 4 Electric Flux and
Gausss Law

• Electric flux ( ? ) product of electric field
  (E) strength times area (A) it passes through.
  Three cases

• E ? A
• (perpendicular)

• E ? A
• (tilted)

3. Non-uniform E
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Example Electric flux through two connected
half-spheres of radii r and R centered on point
charge q.
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Example Electric flux through sphere of radius
r centered on point charge q.
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Gausss Law

• Question would the answers be different if the
  point charge were a small conductor carrying a
  surface charge q rather than an insulator of
  charge q?
• Answer

• Equation
• Reading this in English The net flux through
  ANY closed surface surrounding a charge is the
  same.
• Corollary If a closed surface has no net
  charged enclosed in it, then there is no net flux
  through that surface.

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Example Find E surrounding a point charge at a
distance r by using Gauss Law

• Choose Gaussian surface as sphere centered at q
• Write Gauss Law
• E ?? A everywhere
• E uniform on surface

• Use surface area of sphere
• Substitute in for k
• Solve for electric field

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Example Find E surrounding an infinite line
charge at a distance r by using Gauss Law

• Choose Gaussian surface of cylinder around line
• Write Gauss Law
• E ?? A on sides, E // A on ends
• E uniform on sides

• Use surface area of cylinder
• Substitute in for k
• Define charge enclosed
• Solve for electric field

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Example Find E next to an infinite plane charge
by using Gauss Law

• Choose Gaussian surface of cylinder ? to plane
  with end area A
• Write Gauss Law
• E ?// A on sides, E ? A on ends
• E uniform on ends

• Use surface area of ends
• Substitute in for k
• Define charge enclosed
• Solve for electric field

Note this result also applies to the region just
outside a conductor, where the conductor looks
like a plane charge from an infinitesimal
distance.