16 Overview

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16 Overview
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• work, energy, voltage
• relation between field and voltage
• capacitance
• homework
• 4, 8, 9, 13, 19, 40, 41, 55, 69, 82, 95, 97

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Electrostatic Potential Energy, UE Electric
Potential, V
0

• Charge-charge interaction stores energy
• Ex. two close have high UE
• Electric Potential V is energy per test charge
  in (J/C V) (volts)
• Two steps to find V at a point of interest P
• 1) Measure DUE when q is moved to P (from far
  away)
• 2) Calculate V DUE/q
• /

3
Work-Energy Theorem

• Relates change in energy stored in a system to
  work done by that system.
• DUE -WE
• If positive work is done by an electric system,
  then the change in the stored energy is negative.

4
Example V calculation

• q 1.0 C moved close to another charge
  (from far away).
• If DUE 3.0 J,
• Then V DUE/q (3.0 J)/(1.0 C)

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Point Charge Potential, VQ

• VQ kQ/r
• Ex. Potential 2.0m from Q 4.0nC is VQ kQ/r
  (9E9)(4E-9)/(2) 18V.
• Electric Potential is near charges
• Ex. Potential 4.0m from Q -4.0nC is VQ kQ/r
  (9E9)(-4E-9)/(4) -9V.
• Electric Potential is - near -charges
• /

6
Potential Due to Several Charges

• Point charge potentials add algebraically
• VP VQ1 VQ2
• Ex. If P is 2.0m from Q1 4nC and 4.0m from
  Q2 -4nC, Then

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Potential Difference Average Electric Field
0

• Let test charge q move in the direction of the
  field E (q 0)
• DUE -WE
• DUE -FEd
• DUE -qEavd

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Ex. Average Electric Field
0
X(m) V(volts)
0 100
2 90
10 80
30 70
50 65
Interval
0 to 2
2 to 10
10 to 30
30 to 50
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Equipotential Surfaces
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• surfaces which have the same potential at all
  points.
• Ex. A sphere surrounding an isolated point charge
  is an equipotential surface.
• Ex. A charged conductor in electrostatic
  equilibrium is an equipotential surface. (this
  also implies E near surface is perpendicular to
  the surface)

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Capacitance Charge Stored per Volt Applied
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The capacitance is defined as C Q/V
Units C/V farad F
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Capacitors

• store energy and give it back fast, e.g. flash
  unit

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Permittivity

• Relates to ability of material to store
  electrostatic potential energy
• Empty space value
• Material values are
• k is the dielectric constant
• Exs. k 1.0 air, 3.5 paper

13
Parallel Plate Capacitance

• Ex. Area A 100 square-cm, d 1mm

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Energy Stored in a Capacitor
Charge Q added to Capacitor over average
potential of V/2
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Capacitor Energy
16
Supercapacitors

• Porous structure with high internal surface area
  (A) and small spacing (d) resulting in very large
  capacitance
• Have capacitances greater than 1 farad

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Capacitor Circuits

• Parallel each gets potential V, so capacitance
  increases
• Series each gets potential less than V, so
  capacitance decreases

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Capacitors in Parallel Arrangement
0
Ex.
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Capacitors in Series Arrangement
0
Q 0
Ex.
20
Summary

• Welectric qEd -DEPE
• V DEPE/q
• V V1 V2
• Eavg -?V/d
• C q/V KeoA/d
• Capacitor Energy ½CV2
• Capcitors in series parallel