Electric%20Field%20Lines

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• Electric Field Lines
• Eletric Dipoles
• Torque on dipole in an external field
• Electric Flux
• Gauss Law

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Electric Field Lines

• Electric field E(r) is a vector field.
• How do we visualize a field?
• Show the properties of an electric field by
  drawing the Electric field lines
• An electric field line pattern indicates both the
  magnitude and direction of the field.

Point Charge
Gravitational Field
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Electric Field Lines

• Direction
• Field lines start on positive charges and end on
  negative charges.
• At any point, draw a tangent to the field line.
• This gives the direction of the E-field at that
  point.
• This is also the direction of the force at that
  point.
• Strength
• Given by the number of lines per unit area
  through a plane perpendicular to the field lines.
• Field is the strongest where the lines are close
  together and weakest where they are far apart
• If the lines are uniformly-spaced and parallel,
  the field is uniform.
• Field lines cant cross!

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Conducting Plane
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Two Point Charges
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Electric Dipoles

• Dipole Two equal and opposite charges separated
  by length
• Example water molecule.
• Charge separation from uneven
• sharing of electrons by the 2 atoms
• Dipole moment (points from to )
• Polar molecules have a non-zero dipole moment
• Water (electron shifted ?by ? 4x10-11m,
  Q1.6x10-19 C)
• Water is polar, methane is not
• In addition, insulators will generally develop a
  dipole moment in the presence of an electric
  field.

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Electric Dipoles

• Dipole placed in an electric field
• Experiences zero net force
• Experiences a torque
• If the dipole is free to move then the effect of
  torque is to align the dipole with

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Electric Dipoles

• Since positive work is done by the field to align
  the dipole, the potential energy of the dipole
  decreases
• Potential Energy
• Maximum PE when is anti-parallel (opposite)
  to
• Minimum PE when and are in the same
  direction
• Conventional to take potential energy to be zero
  when
• (remember only changes in potential energy are
  measurable, so we have freedom to choose where
  U0)

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Sakurajima Volcano

• Streaks of lightning
• Is the origin same as lightning accompanying
  thunderstorms?

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Chapter 22 Gauss Law
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Electric Flux

• Flux (origin Latin to flow)
• Number of something penetrating a surface.
  (webster)

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Electric Flux

• Flux (origin Latin to flow)
• Number of something penetrating a surface.
  (webster)
• Electric flux is a measure of the number of
  electric field lines passing through a surface

Direction of Area vector A is normal to the
plane of area
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Example

• An arbitrary closed surface immersed in an
  electric field.

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Gauss Law

• An alternative formulation of Coulombs law to
  compute the E-field due to a distribution of
  charges.
• The integral method of calculating electric field
  is conceptually simple but can be difficult to
  implement.
• Gauss' Law can be a very powerful and an easy
  alternative if one can take advantage of the
  geomteric symmetry of the problem.
• example E-field due to a long line of charge

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Karl Friedrich Gauss (1777-1855)
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Gauss Law

• Gauss' Law states that the net electric flux
  through a closed surface is proportional to the
  charge enclosed by the surface, qenc.
• Net flux
• The integral here is over the surface.
• The area vector points out from the surface.
• The constant ?0 is known as the permittivity of
  free space, and is given by
• ?0 1/(4? k) 8.85 x 10-12 C2 N m2

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Gauss Law

• The more charge enclosed, the greater the flux
  through the surface.
• The net flux is positive if the net charge
  enclosed is positive, and negative if the net
  charge enclosed is negative.
• If there is no net charge enclosed by a surface
  the net flux is zero - any field lines entering
  the surface must leave the surface somewhere
  else.

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Example point Charge

• Electric Field due to a point charge (Coulombs
  Law)
• Field from a point charge q is radial
• field lines are directed along radii, directly
  out from or into the charge
• Electric Flux
• Independent of radius of the sphere

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Electric FluxCounting Field Lines through a
surface

• Lets observe the number of field lines passing
  through the surface in different situations.
• We note
• If a surface encloses a net positive charge then
  more field lines come out of the surface than go
  into it
• If a surface encloses a net negative charge then
  more field lines go into it than come out
• If a surface encloses either no charges or equal
  numbers of positive and negative charges (ie zero
  net charge) then the same number of filed lines
  come out of the surface as go into it.
• It appears that the number of field lines through
  a surface is proportional to the net charge
  enclosed by the surface (Gauss Law)