16'2 Equipotentials Capacitance

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16.2 EquipotentialsCapacitance

• Equipotential surfaces
• Capacitance of parallel plate capacitor

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Electron volt- unit of energy
?PE q?V Where qe 1.6x10-19C 1eV
1.6x10-19 J Useful for atomic properties.
The potential at Na due to Cl- was -6.0V. Energy
of Na ion at this position is PEeV-6.0
eV PE-6x1.6x10-19 9.6x10-19J

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Equipotential Surface - positions in space at
which the electrical potentials are equal
Example 1- A sphere centered around a point charge
Every point on the surface of the sphere of
radius r has the same potential
Vkeq/r
r
q
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Equipotential surface-
Example 2 a charged conductor
The surface of a conductor is an equipotential
surface.
E


E field is perpendicular to the surface.

• Component of E 0 parallel to the surface
• ?VEd0
• No change in potential along the surface

equipotential
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The interior of the conductor is an equipotential
and at the same potential as the surface.


E0 in the conductor Thus, the potential doesnt
change from the surface potential
V



V
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The equipotential surfaces are perpendicular to E
field lines.
Equipotential
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Draw a sketch of the equipotential surfaces for a
electric dipole q q.
V0
Vgt0
Vlt0
-q
q
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Capacitance
Capacitor- a device for storing charge (energy) -
can be discharged rapidly to release
energy Examples. Camera flash, capacitor in
automobile starting system, capacitors in
electronic devices
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Parallel Plate Capacitor Metal plates separated
by an air gap
q
A
?V
d
-q
Capacitance
Units C/V farad (F)
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A 100 microfarad capacitor is charged to 100 V.
How much charge does it store?
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What is the capacitance of a parallel plate
capacitor with plates of area A separated by
distance d?
q
A
?V
d
-q
Recall
rearrange
thus
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• A parallel plate capacitor with 2 plates each
  with area 1.0 m2 separated by a distance of 1.0
  mm.
• Find the capacitance.
• Find the E field if the plates hold q,-q,
  q10-6C
• Find ?V across the plates

(a)
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• A parallel plate capacitor with 2 plates each
  with area 1.0 m2 separated by a distance of 1.0
  mm.
• Find the capacitance.
• Find the E field if the plates hold q,-q,
  q10-6C
• Find ?V across the plates

(b)
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• A parallel plate capacitor with 2 plates each
  with area 1.0 m2 separated by a distance of 1.0
  mm.
• Find the capacitance.
• Find the E field if the plates hold q,-q,
  q10-6C
• Find ?V across the plates

(c)
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A parallel plate capacitor with 2 plates each
with area 1.0 m2 separated by a distance of 1.0
mm, and charge q.

• If the distance between the plates was increased
  by a factor of 2 how does E change?
• How does ?V change?

These are all constant. Thus, E is unchanged
(a)
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A parallel plate capacitor with 2 plates each
with area 1.0 m2 separated by a distance of 1.0
mm, and charge q.

• If the distance between the plates was increased
  by a factor of 2 how does E change?
• How does ?V change?

E is constant d increases by 2-fold thus ?V
increases by 2-fold
(b)