Maxwell and Faraday

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Maxwell and Faraday
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Temperature Map
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Barometric Pressure Map
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Java Script
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Electric Fields

• A vector field is a vector valued function
  defined throughout space,
• i.e. it defines a vector at every point in 3-D
  space

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A test charge is, by definition,
infinitesimal. It is so small that it does not
affect the E field locally.
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Keep in mind the distinction between the source
point and the field point where E is evaluated
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(22-10)
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Field Lines

• Tanget lines to the E field vectors
• Start on charge and end on -
• Can start or end at infinity
• Number of lines proportional to charge
• Density of lines proportional to field magnitude

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Dipole Field
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Field Lines

• Always perpendicular to conducting surface
• End/start at conducting surface

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• Interior of a metal in equilibrium has zero
  electric field, if not E0 the charges would
  redistribute themselves.
  

All charge resides on the outside of the
conductor, E field must be perpendicular to the
surface. The interior of a hollow conductor also
obeys E0.
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Think About It

• Can field lines cross?

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The Answer

• No, becase then the E Field would have to go two
  different directions from the same point, which
  is unphysical.

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Think About This

• Give an argument that the E field at the apex of
  a conical hole drilled in a conductor must be
  zero.

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• Field lines must be perpendicular to the metal,
  and would need to point two directions from the
  same point at the apex.

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• Conversely field is stronger where the metal is
  pointed. Thats why lightning rods work. The
  air breaks down at the tip of the rod where the
  field is large.

Franklin designed lightning rod.
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Why are Van de Graf and other Electro-static
generators rounded?
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Coulomb Force in 2-D
Coulomb Force in 3-D
Substitute q0 for qB and divide through to find E
field components
E Field in 2-D ltxf , yfgt is the field point
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In 3-D the field at ltxF, yF, zFgt due to charge qA
at point ltxA, yA, zAgt
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In 3-D the field at ltxF, yF, zFgt due to charge qA
at point ltxA, yA, zAgt
In 3-D the field at ltxF, yF, zFgt due to multiple
charges qi at points ltxi, yi, zigt
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Dipole Field
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Using the Binomial theorem (page A-10) we could
reduce this to
The details of the calculation are
at http//www.phy.olemiss.edu/kroeger/PHY212/dip
ole_E.pdf
In polar coordinates it looks like
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How do we go over to continuous distributions of
charge?
dq
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Worked out for a straight line charge
http//www.phy.olemiss.edu/kroeger/PHY212/Linear_
Charge_E.pdf
Radial component of force due to linear charge of
length L at a point a distance y radially from
middle of segment
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For uniformly charged disk this is performed at
http//www.phy.olemiss.edu/kroeger/PHY212/E_Disk
.pdf
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Field due to volume distribution of charges
Ugly, but in principle you can do it.