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Chapter 14, MHR-Fields and Forces
Chapter 17 Giancoli Electrical Potential
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Today’s Topics
• Electric Potential Energy
• Electric Potential
• Electric Equi-potential Lines
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Work
• You do work when you push an object up a hill• The longer the hill the more work you do: more
distance• The steeper the hill the more work you do: more
force
The work W done on an object by an agent exerting a constant force is the product of the component of the force in the direction of the displacement and the magnitude of the displacement
dFW ||
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Work done by gravity
cosFdW
m
mg
d
cosF
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Energy is capacity to do worknote Ep aka UG
• Gravitational Potential Energy
• Kinetic Energy
• Energy can be converted into other forms of energy
• When we do work on any object we transfer energy to it
• Energy cannot be created or destroyed
mghUG 2
2
1mvK
GU
GUKW
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• A person lifts a heavy box of mass ‘m’ a vertical distance ‘h’
• They then move a distance ‘d’, carrying the box
• How much work is done carrying the box?
Quiz
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Conversion of Gravitational Potential Energy to Kinetic
Energym
mg
m
v
mghUG 2
2
1mvK
ghv
ghv
mghmv
2
2
2
1
2
2
Work done on object
h
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What’s an electric field?
• A region around a charged object through which another charge will experience a force
• Convention: electric field lines are drawn out of (+) and into (-); so the lines will show the movement of a “positive test charge”
• E = F / q • units are in N/C
+Q
+Q
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Electric Potential Energycharges also have electrical potential energy
EEF Q
+Q
+Q
d
FdW
QEd
QEdU e
v
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Electric Potential Energy
• Work done (by electric field) on charged particle is QEd
• Particle has gained Kinetic Energy (QEd)
• Particle must therefore have lost Potential Energy U=-QEd
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Electric Potential
The electric potential energy depends on the charge present
We can define the electric potential V which does not depend on charge by using a “test” charge
EdQU 0
0Q
UV
Change in potential is change in potential energy for a test charge per unit charge
EdQ
UV
0
for uniform field
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Electric Potential
0Q
UV
compare with the Electric Field and Coulomb Force
0Q
FE
If we know the potential field this allows us to calculate changes in potential energy for any charge introduced
VQU EF Q
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Electric Potential
Electric Potential is a scalar field
it is defined everywhere
but it does not have any direction
it doesn’t depend on a charge being there
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Electric Potential, units
SI Units of Electric Potential
0Q
UV
EdV
Units are J/C
Alternatively called Volts (V)
We have seen
dVE / Thus E also has units of V/m
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Potential in Uniform field
E
+Q +Q
+Q
A B
C
0|| dFWBC
|||| QEddFWAB
BCABAC WWW
||QEd
||QEdU AC d||
||EdVAC
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Electric Potential of a single charge
+
r
E
B
A
Advanced
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Equi-potential Lines
Like elevation, potential can be displayed as contours
A contour diagram
Like elevation, potential requires a zero point, potential V=0 at r=
Like slope & elevation we can obtain the Electric Field from the potential field
r
VE
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Potential Energy in 3 charges
r
QV
04
1
Q2
Q1
Q3
12
1
02212 4
1
r
QQVQU
12
21
012 4
1
r
QQU
23
2
13
1
03123312 4
1
r
Q
r
QQUVQUU
231312 UUUU
23
32
13
31
12
21
04
1
r
r
r
QQU
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Capacitors
A system of two conductors, each carrying equal charge is known as a capacitor
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-
Capacitance of charged sphere
+Q
r=
V
QC
definition
R
r
QV
0 4
1
potential due to
isolated charge
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Capacitors
-
+ +Q -Q
e.g. 1: two metal spherese.g. 2: two parallel sheets
Each conductor is called a plate
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CapacitanceCapacitance…….. is a measure of the amount of charge a capacitor can store (its “capacity”)
Experiments show that the charge in a capacitor is proportional to the electric potential difference (voltage) between the plates.
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Units
V
QC
Thus SI units of capacitance are:
C/V
This unit is also known as the farad after Michael Faraday
Remember that V is also J/C so unit is also C2J-1
1F=1C/V
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Capacitance
The constant of proportionality C is the capacitance which is a property of the conductor
VQ VCQ V
QC
Experiments show that the charge in a capacitor is proportional to the electric potential difference (voltage) between the plates.
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Capacitance of parallel plates
+Q -Q
Intutively
The bigger the plates the more surface area over which the capacitor can store charge C A
E
Moving plates togeth`er Initially E is constant (no charges moving) thus V=Ed decreases charges flows from battery to
increase V C 1/d Never Ready+
V
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Batteries, Conductors & Potential
Never R
eady
+A battery maintains a fixed potential difference (voltage) between its terminals A conductor
has E=0 within and thus
V=Ed=0
VV= 0
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Capacitance of parallel plates
+Q -Q
Physically
E
Never Ready+
EdV
V
QC
property of conductorV
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