CAPACITANCE III

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CAPACITANCE III
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RECAP

• The electrostatic energy stored in the capacitor

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• Capacity increases if the dielectric material is
  introduced.
• If the battery is connected
• If the capacitor is charged, disconnected from
  battery, and then dielectric is introduced

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Capacities with the dielectric

• Parallel plate capacitor
• Spherical capacitor
• Cylindrical capacitor

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Electrostatic pressure

• Force on a plate of capacitor

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Todays plan

• Energy stored before and after the dielectric is
  filled.
• Force on a dielectric

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Energy stored before and after

• Before ?
• Since C kC0
• Why Ult U ?? Where does this energy go?

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Reason

• Dielectric, when inserted, gets pulled into the
  device. External agent do negative work to
  prevent the dielectric from accelerating.
• Work U?-U

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The nonuniform electric field (fringing field)
near the edges causes a dielectric to be pulled
into the capacitor.
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Fringing Field
The bound charges tend to accumulate near the
free charges of opposite sign.
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If no external agent works, slab will be
accelerated.
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Slab oscillates between the ends
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Slab oscillates between the ends
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Slab oscillates between the ends
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Slab oscillates between the ends
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Slab oscillates between the ends
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To calculate the force due to electric field on
the dielectric material
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Let the external agent pulls the dielectric out
by a infinitesimal displacement dx

• Plate area is L x L

x
Fext
dW Fext dx Fext dW/dx Electric force on
the dielectric -Fext
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Charge on the plates is constant
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If the battery maintains a constant potential
The force simply depends only upon the fringing
field and free and bound charges
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Two coaxial metal tubes stand vertically in a
tank of dielectric oil (susceptibility ?e and
mass density ?. Tubes are maintained at a
potential difference of V. To what height (h)
does the oil rise in the space between the tubes.

Problem
Griffiths Problem 4.28, page 196 vol 3.
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Calculate the electrostatic energy stored between
the plates of the cylindrical capacitor using the
relation
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r a to b ? 0 to 2? Z 0 to L
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Problem 4.21 Griffiths

• A certain coaxial cable consists of a copper wire
  , radius a , surrounded by a concentric copper
  tube of inner radius c. The space between is
  partially filled (from b out to c) with a
  material of dielectric constant ke. Find the
  capacitance per unit length of this cable.

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Find the capacitance per unit length of this cable
Dielectric Material
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A parallel plate capacitor is filled with a
dielectric of dielectric constant ke. The ke
varies parallel to an edge as

• Where x is the distance from the left end.
  Calculate the capacitance.

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Find the Ceq
Twelve capacitors, each have capacity C are
connected to form a cube.
B
A
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B
F
A
E
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B
Isolated system Total charge zero
Q/3
F
Q/6
A
E
Q/3
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B
Q/3
F
Q/6
A
E
Q/3
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