Lecture 6 Capacitance and Capacitors Electrostatic Potential Energy

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Lecture 6Capacitance and CapacitorsElectrostat
ic Potential Energy

• Prof. Viviana Vladutescu

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Capacitance

• A conductor in electrostatic field is
  equipotential and charges distribute themselves
  on the surface such way that E0 inside the
  conductor Q on the surface is producing V
  

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linear dependence
kC
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Capacitance (of the isolated conducting body) -
is the electric charge that is added to the body
per unit increase in its electric potential (is a
constant of proportionality)
Depends on the geometry of the conductors
-the dielectric constant of the
medium between conductors

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Capacitors
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Electrolytic capacitors
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Determine capacitance

• 1- assume Vab Q (in terms of Vab)
• use boundary conditions
• 2- assume Q Vab (in terms of Q)

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Q Vab

• Step 1Chose coordinate system for given geometry
• Step 2 Assume Q and Q on the conductors
• Step 3 Q E from DeE?s or
• Step 4 E
• Step 5 CQ/Vab

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Example
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Vab Q

• Step 1Chose coordinate system for given geometry
• Step 2 Assume Vab between plates
• Step 3 Vab E D (from Laplaces
  equation)
• Step 4 Boundary conditions at each plate
• conductor dielectric boundary
• ?s
  Q
• . Step 5 CQ/Vab

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Example
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There is no f and z variation
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Step 4
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Q on the inner conductor
Step 5
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Series Connected Capacitors
Parallel Connected Capacitors
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Electrostatic Potential Energy
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• Electric potential at a point in an electric
  field is the work required to bring a unit
  positive charge from infinity (at reference zero
  potential) to that point.

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Now suppose we want to bring Q3 at R13 from
Q1 and R23 from Q2
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-can be negative -represents only interaction
energy
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For a group of N discrete charges at rest
For a continuous charge distribution of density ?
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Electrostatic energy in terms of field quantities
Substitute ?
And by using
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Electrostatic Energy Density
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Example
Along AB, W -q?V zero!

Equipotential surfaces are at right angles to
the electric field. Otherwise a force would act
and work would be done on the path A to B.For a
uniform electric field, equipotentials form
planes perpendicular to the field.