Chapter 14, MHR-Fields and
Forces
Chapter 17 Giancoli Electrical
Potential
Today’s Topics
• Electric Potential Energy
• Electric Potential
• Electric Equi-potential Lines
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
W  F||d
Work done by gravity
d
W  Fd cos
mg

F cos
Energy is capacity to do work
note Ep aka UG
• Gravitational Potential Energy U G  mgh
1
• Kinetic Energy
K  mv
2
• Energy can be converted into other forms of
energy
  U G
• When we do work on any object we transfer
W  K  U G
energy to it
• Energy cannot be created or destroyed
2
Quiz
• 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?
Conversion of Gravitational
Potential Energy to Kinetic
Energy
U G  mgh
m
h
mg
1 2
K  mv
2
1 2
mv  mgh
2
v 2  2 gh
v  2 gh
Work done on object
m
v
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”
+Q
• E=F/q
• units are in N/C
+Q
Electric Potential Energy
charges also have electrical potential energy
W  Fd
+Q
E
 QEd
F  QE
d
U e  QEd
+Q
v
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
Electric Potential
The electric potential energy depends on
the charge present
We can define the electric potential
V which does not depend on charge
Change in potential is
by using a “test” charge
change in potential energy
for a test charge per unit
charge
U
V 
for uniform field
U  Q0 Ed
Q0
U
V 
  Ed
Q0
Electric Potential
compare with the Electric Field and Coulomb Force
U
V 
Q0
F
E
Q0
U  QV
F  QE
If we know the potential field this allows us to
calculate changes in potential energy for any
charge introduced
Electric Potential
Electric Potential is a scalar field
it is defined everywhere
it doesn’t depend on a charge being there
but it does not have any direction
Electric Potential, units
SI Units of Electric Potential
U
V 
Q0
Units are J/C
Alternatively called Volts (V)
We have seen
E  V / d
V  Ed
Thus E also has units of V/m
Potential in Uniform field
WBC  F||d  0
E
C
+Q
WAB  F||d  QEd ||
WAC  WAB  WBC
 QEd ||
d||
+Q
+Q
A
B
U AC  QEd ||
V AC   Ed||
A
Electric Potential of a single
charge
E
B
r
+
Equi-potential Lines
Like elevation, potential can be displayed as contours
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
V
E
r
A contour diagram
Potential Energy in 3 charges
Q2
Q1
U12  Q2V  Q2
U12 
Q3
U  U12  U13  U 23
1 Q1
40 r12
1
Q
V

40
r
1 Q1Q2
40 r12
1  Q1 Q2 
U  U12  Q3V3  U12  Q3
  
40  r13 r23 
1  Q1Q2 Q1Q3 Q2Q3 
U




40  r12
r13
r23 
Capacitors
A system of two conductors, each
carrying equal charge is known as
a capacitor
Capacitance of charged sphere
Q
C
V
40 r
V 
1 Q
r=
R
+Q
-
definition
potential due to
isolated charge
Capacitors
e.g. 1: two metal spheres
e.g. 2: two parallel sheets
+
Each conductor is called a plate
+Q
-Q
Capacitance
Capacitance…….. 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.
Units
Q
C
V
Thus SI units of capacitance are:
C/V
Remember that V is also
J/C so unit is also C2J-1
This unit is also known as the farad
after Michael Faraday
1F=1C/V
Capacitance
Experiments show that the charge in a
capacitor is proportional to the electric
potential difference (voltage) between the
plates.
The constant of proportionality C is
the capacitance which is a property
of the conductor
Q  V
Q  CV
Q
C
V
Capacitance of parallel plates
V
E
+
+Q
Never Ready
-Q
Intutively
The bigger the plates the
more surface area over
which the capacitor can
store charge C  A
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
Batteries, Conductors & Potential
+
Never Ready
V
A battery maintains a
fixed potential
difference (voltage)
between its terminals
V= 0
A conductor
has E=0
within and
thus
V=Ed=0
Capacitance of parallel plates
V
Physically
property of conductor
E
+Q
-Q
V  Ed
+
Q
C
V
Never Ready