Chapter 20
Electric Forces and Fields
Topics:
• 
• 
• 
• 
Electric charge
Forces between charged
objects
The field model and the
electric field
Forces and torques on
charged objects in electric
fields
Sample question:
In electrophoresis, what force causes DNA fragments to migrate
through the gel? How can an investigator adjust the migration rate?
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Slide 20-1
What to do to do well in this class
A. Focus on key physics concepts
•  May seem like basics but will help you solve even complex
problems
•  Focus on principle rather than recipes
•  Need to have a functional understanding of key concepts
•  Express key equations as sentences
•  Know where they come from and what they mean
•  Know how and when to apply them
•  Know which equations are general and which are special cases
•  Must know when not to apply special cases
•  Look at a problem after a good physics diagram and maybe a
good physical diagram and know what key physics concepts apply
in that problem
•  Memorize key concepts so you can look at a problem, say that s
Newton 2, and know the associated equation in a snap
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Slide 21-16
What to do to do well in this class
A. Focus on key physics concepts
•  How to do this
•  When you look at problems, mentally group problems by
the physics rather than the physical situation
•  After each class or at least each week, create a notesheet
to organize a structure of the new key concepts for each
chapter and note how they fit in with previous key concepts
•  Use the note sheet to do homework problems (a) do as
many homework problems as you can just using this
sheet. (b) then go to your notes and the textbook for your
missing pieces
•  Use flash cards to memorize key concepts - include the
concept description, relevant equations, diagrams, and
what types of problems benefit from using that concept
•  Pay close attention to examples done in class and note the
physics and assume/observes in each example and how
these are used
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Slide 21-16
Nature of Electric Field Vectors
•  Test charge is a small positive charge to sample the E-Field
•  Charge of test charge is small compared to source charges
(source charges are the charges that generate the E-field)
•  E-field vectors
•  E -field is the force per charge
•  E-field vectors points away from + charges
•  E-field vectors point towards - charges
•  E -field for point charges gets weaker as distance from source
point charges increases
•  E-fields add as vectors, at a point in space Enet,x = E1x + E2x + …
•  For a point charge E = Fe / |q| = [k |Q| |qt| / r2] / |qt| = k |Q| / r2
•  Electric Force
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Nature of Electric Field Lines
•  E-Field lines start on + charges and end on -- charges
•  Larger charges will have more field lines going out/coming in
•  Density of Field lines is a measure of field strength – the higher
the density the stronger the field
•  The E-field vector at a point in space is tangent to the field line
at that point. If there is no field line, extrapolate.
•  Note: E-field lines represent the force a test object would feel
at that point; however, test objects do not necessarily move
along field lines.
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Consider an infinite sheet of charge
!
Q
E=
where ! =
2"0
A
•  Epsilon nought, ! 0 = 8.85 " 10
#12
2
C
N $ m2
is electric permitivity of free space
•  Electric permitivity is a measure of how well
electric field can pass through space or
material
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Consider two infinite sheets of charge
What is the E-field at
points A, B, and C ?
Case 1:
A
B
C
Qleft = +Q
Qright = -Q
Case 2:
Qleft = 2Q
Qright = Q
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Conductors and Electric Fields Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 20-55
Forces and Torques on Charges in Electric Fields
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Slide 20-56
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Slide 20-5
Checking Understanding
A dipole is held motionless in a uniform electric field. For the
situation below, when the dipole is released, which of the following
describes the subsequent motion?
A.  The dipole moves to the right.
B.  The dipole moves to the left.
C.  The dipole rotates clockwise.
D.  The dipole rotates counterclockwise.
E.  The dipole remains motionless.
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Determining the E field produced
by given source charges
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E-field Superposition Example
1.  Determine the magnitude and the direction of the electric field
at point A.
In your physical diagram, make sure you label your
r s
as well as your angles
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E-field Superposition Examples
1.  Determine the magnitude and the direction of the electric field
at point A.
2.  Determine the individual forces and the net force on charge B
for each of the following cases.
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Slide 20-66
Example Problem 1
• Two small metal spheres attached to
insulating stands reside on a table a distance
d apart. The left sphere has positive charge
+q and the right sphere has negative charge
−q. Determine the magnitude and direction
for the E field at a distance d above the
center of the line connecting the spheres.
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Problem-solving strategy: Incorporating the E field into Newton's second law
• In the ”Prepare" step, be sure to determine
the E field produced by the environment. Is
it produced by point-like charges (making it
non-uniform) or by large charged plates
(making it uniform)?
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Example Problem 2
• Inside an inkjet printer, a tiny ball of black
ink of mass 1.1 x 10−11 kg with charge −6.7 x
10−12 C moves horizontally at a speed of 40
m/s. The ink ball enters an upward-pointing
uniform E field of magnitude 1.0 x 104 N/C
produced by a negatively charged plate
above and a positively charged plate below.
The plates deflect the ink ball so that it lands
at a particular spot on a piece of paper.
Determine the deflection of the ink ball after
it travels 0.010 m in the E field.
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Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Types of Energy
Conservation of Energy Equation (key concept)
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Slide 21-16
Dot Product
Dot product or scalar product is a way of multiplying
two vectors to get a scalar result
Dot products can be calculated
either independent of
!
a coordinate system where ! is the angle between
the two vectors
! ! ! !
A ! B
= A B cos "
Note that in this vector form the sign of the dot
product only depends on the angle Component form of Dot Product
! !
A ! B = Ax Bx + Ay By + Az Bz
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Slide 4-19
Dot Product: Example 1
Dot product or scalar product is a way of multiplying
two vectors to get a scalar result
Dot products can be calculated
either independent of
!
a coordinate system where ! is the angle between
the two vectors
! ! ! !
A ! B = A
B cos "
Vector A has a magnitude of 4 units
Vector B has a magnitude of 3 units
Angle between them = 60 degrees
! !
A ! B = 4 units " 3units " cos(60°) = 6 units
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Chapter 21 Key Ideas (Physics 151)
Dot Product
Method for multiplying two vectors to get a scalar
Definition of Work
Work is how forces add energy to or take away energy from a
system. It is the effect of a force applied over a displacement.
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Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Definition of Work
!
! ! !
Work!!W = F!i!!r = F !r cos "
Where ! = angle between the vectors
Work- Energy Theorem (only valid when particle model applies)
Wnet = !KE
Work done by a conservative force (Fg, Fs, & Fe)
Wg = !"PEg Also work done by conservative force
is path independent
Conservation of Energy Equation
KEi +
!
PEi + " Esys = KE f +
different !types
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!
PE f + "Eth
different !types
Slide 21-16
Energy Bar Graph Sample
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Energy Bar Chart Example 1
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Energy Bar Chart Example II
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Energy Bar Chart Example III
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Review of Work
!
! ! !
Definition of Work: Work!!W = F!i!!r = F !r cos "
where ! = angle between the vectors
•  Calculate the work done in moving each ball from y = 0 meters to y = 5 meters
•  Calculate the work per kg for moving each ball from y = 0 m to 5 m
•  Calculate the change in gravitational potential energy per kg for moving each
ball from = 0 m to 5 m
•  Calculate the speed each ball would have as it reached the ground if released
from 5 meters above the ground
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Slide 21-16
Electric potential energy: A qualitative analysis
•  A positively charged
cannonball is held near
another fixed positively
charged object in the
barrel of the cannon. •  Some type of energy must
decrease if gravitational
and kinetic energies
increase in this process.
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Electric Potential Energy
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Slide 21-9
Electric Potential Energy
Case A - Book starts & stops at rest
WNet = !EK = 0J
Whand + Wg = 0 ! Whand = "Wg = #Eg
Case C - Charge at rest at A and B
WNet = !EK = 0J
Whand + We = 0 ! Whand = "We = #Ee
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Slide 21-9
Chapter 21 Key Equations (2)
Key Energy Equations from Physics 152
q1q2
PEe = k
r12
Electric Potential Energy for 2 point charges
(zero potential energy when charges an infinite distance apart)
D Potential Energy for a uniform infinite plate
!
!
%
!PEe = "We = " & Fe # !r cos $ '( = " ( q E ) !r cos $
For one plate, zero potential energy is at infinity
For two plates, zero potential energy is at one plate or
inbetween the two plates
Electric Potential V and Change in Electric Potential => Delta V
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Slide 21-16
Graphing the electric potential energy versus distance
•  Because of the 1/r dependence, the electric potential
energy approaches positive infinity when the
separation approaches zero, and it becomes less
positive and approaches zero as like charges are
moved far apart.
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Example: Electric Potential Energy
A cart on a track has a large, positive charge and is located between
two sheets of charge. Initially at rest at point A, the cart moves
from A to C.
a.  Draw qualitative force diagrams for
the cart at positions A, B and C.
b.  Draw qualitative energy bar charts
for the cart when it is at each position
A, B and C. List the objects that
make up your system:
c. How would your force and energy diagrams change (if at all) if the sheet to
the right were also positively charged?
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Slide 21-16
Changes in Electric Potential Energy - Delta PEe
For each situation below, identify which arrangement (final or initial) has more
electrical potential energy within the system of charges and their field.
Initial (A)
Final (B)
(a)
Greatest Delta PEe
(b)
(c)
(d)
Hydrogen Atom
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Slide 21-16
Changes in Electric Potential Energy – Delta PEe
For each situation below, identify which arrangement (final or initial) has more
electrical potential energy within the system of charges and their field.
Initial (A)
Final (B)
(e)
(f)
Greatest Delta PEe
(g)
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Slide 21-16
Changes in Electric Potential Energy – Delta PEe
Is the change ∆PEe of a + charged particle positive, negative,
or zero as it moves from i to f?
(a) Positive (b) Negative (c) Zero (d) Can t tell
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Slide 21-11
Electric Potential Model Worksheet 2: Energy and Potential in Uniform Fields
"
Rank the change in gravitational potential energy for the following lettered objects in the
Earth s gravitational field.
a. . most  _______ _________ ________ ________ _______ _______ ________
b. Explain your ranking, stating why each is greater than, less than, or equal to its
neighbors.
c. Where is the energy stored? What gains or loses energy as the masses move from one
place to another?
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Slide 21-16
Electric Potential Energy Example Problem
The electric field between two
charged plates is uniform with a
strength of 4 N/C.
a. Draw several electric field lines in the
region between the plates.
b. Determine the change in electrical
potential energy in moving a positive
4 microCoulomb charge from A to B.
c. Determine the change in electrical potential energy in moving a
negative 12 microCoulomb charge from A to B.
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Slide 21-16
Gravitational Potential Energy: Example Problem 2
A spacecraft is launched away from earth
a. Draw several gravitational field lines
in the region around Earth.
b. Determine the change in
gravitational potential energy when
the spacecraft moves from A to B,
where A is 10 million miles from
Earth and B is 30 million miles from
Earth.
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Slide 21-16
Electric Potential Energy: Example Problem 3
A small charge moves farther from a
positive source charge.
a. Draw several electric field lines in the region
around the source charge.
b. Determine the change in electrical potential
energy in moving a positive 4 nC charge
from A to B, where A is 3 cm from the source
charge and B is 10 cm away.
c. Determine the change in electrical potential
energy in moving a negative 4 nC charge
from A to B.
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Slide 21-16
The V field
• Can we describe electric fields using the
concepts of work and energy? • To do so, we need to describe the electric
field not as a force-related E field, but as an
energy-related field.
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Electric potential due to a single charged object
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Finding the electric potential energy when the V field is known
•  If we know the electric potential at a specific
location, we can rearrange the definition of the V
field to determine the electric potential energy:
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The superposition principle and the V field
due to multiple charges
• where Q , Q , Q , … are the source charges
1
2
3
(including their signs) creating the field and r1, r2, r3,
… are the distances between the source charges
and the location where we are determining the V
field.
• So Electric Potentials (V) add just like Electric Potential Energies
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Quantitative Example
•  Suppose that the heart's dipole charges −Q and +Q are separated
by distance d. Write an expression for the V field due to both
charges at point A, a distance d to the right of the +Q charge.
1.  Simplify and diagram.
2.  Represent mathematically.
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Finding the electric potential energy when the V field is known
•  If we know the electric potential at a specific
location, we can rearrange the definition of the V
field to determine the electric potential energy:
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Potential difference – Delta V
• The value of the electric potential depends
on the choice of zero level, so we often use
the difference in electric potential between
two points.
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Particles in a potential difference
• A positively charged object accelerates from
regions of higher electric potential toward
regions of lower potential (like an object
falling to lower elevation in Earth's
gravitational field).
• A negatively charged particle tends to do the
opposite, accelerating from regions of lower
potential toward regions of higher potential. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.