King Saud University
College of Applied Studies
and Community Service
Department of Natural
Sciences
Electric Field and Electric
Potential
General Physics II
PHYS 111
Nouf Alkathran
1
OUTLINE
• Electric
Charge
o Insulators and Conductors
o Coulomb’s Law
• The Electric Field
Electric Field Lines
o Electric Potential Energy
o Electric Potential
o Electric Potential due to Point Charges
o
2
OUTLINE
Electric Potential due to Collection of Point
Charges
o Potential Energy in Two Points of Charges
o Potential Energy in a System of Charges
o Continuous Charge Distribution
o Potential Difference (voltage)
o Electric Potential in a Uniform Field
o
• Questions
• References
3
Electric Charge
• The effects of electric
charge were first
observed as static
electricity:
After being rubbed on a
piece of fur, an amber rod
acquires a charge and can
attract small objects.
4
Electric Charge
• Charging both amber and glass rods
shows that there are two types of electric
charge; like charges repel and opposites
attract.
5
Electric Charge
6
Electric Charge
• When an amber rod is
Rubbed with fur some of
the electrons on the
atoms in the fur are
transferred to the amber
7
Insulators and Conductors
Conductor
• A material with free
charged
particles that easily flow
through it when electric force
acts on it.
• Conductors are good
conductors of electricity.
• Examples: Metals.
Insulator
• A material whose
electrons
seldom move from atom to
atom. Most insulators are
non-metals
• Insulators are poor
conductors of electricity.
• Examples: Rubber, Glass
and wood.
8
Insulators and Conductors
• SEMICONDUCTORS: A Material with
properties that fall between a conductor
and insulator and whose resistance can be
affected by adding impurities.
• Superconductors: A material that is a
perfect conductor with zero resistance to
the flow of electric charge.
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Conductors
• If a conductor carries
excess charge, the
Excess is distributed
over the surface of
the conductor.
10
Conductors
Charged Conductors
• The absence of electric field within a
conductor holding static charge is not an
inability of an electric field to penetrate
metals.
• Free electrons within the conductor can
“settle down” and stop moving only when
the electric field is zero.
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Coulomb’s Law
1
𝑘=
4𝜋𝜀°
12
Coulomb’s Law
• The force is along the
line connecting the
charges, and is attractive
if the charges are
opposite, and repulsive
if the charges are like.
13
The Electric Field
Electric Field: is force per unit charge.
SI Unit: N/C
Imagine a small positive “test charge” placed in an electric
field.
• Where the force is greatest on the test charge, the field is
strongest.
• Where the force on the test charge is weak, the field is small.
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Electric Field Lines
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Electric Field Lines
• Electric field lines:
1. The lines must begin on a positive charge and
terminate on a negative charge.
2. In the case of an excess of one type of charge,
some lines will begin or end infinitely far away.
3. The number of lines drawn leaving a positive
charge or approaching a negative charge is
proportional to the magnitude of the charge.
4. No two field lines can cross.
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Electric Field Lines
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Electric Field Lines
• Note that the lengths of the arrows are longer
when closer to the source charge and shorter
when further from the source charge.
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Electric Potential Energy
• In an elevated position, the ram has
gravitational potential energy. When released,
this energy is transferred to the pile below.
• Similar energy transfer occurs for electric
charges.
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Electric Potential Energy
(a) A positive test charge 𝒒° ,
experiences a downward force
due to the electric field 𝑬→ . If the
charge is moved upward a distance
d, the work done by the electric
field -𝒒° 𝑬𝒅. At the same time the
electric potential energy of the
system increases by 𝒒° 𝑬𝒅. The
situation is analogous to that of
an object in gravitational field. (b) If
a ball is lifted against a force exerted
By gravity, the gravitational potential
Energy of the system increases.
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Electric Potential Energy
𝑊 = −𝑞° 𝐸𝑑
∆𝑈 = −𝑞° 𝐸𝑑
Where:
W: the work done by electric force(Joule)
U: potential energy (Joule)
D:distance between charges (m)
E: strength of electric field (N/C)
• A charged object can have potential energy by virtue of its location
in an electric field.
• Work is required to push a charged particle against the electric field
of a charged body.
• When an electric field moves a positive charge toward the electric
field, the electric potential energy of the positive charge decreases.
• When an electric field moves a negative charge against the electric
field, the electric potential energy of the negative charge decreases.
21
Note
Electric potential is not the same as
electrical potential energy. Electric
potential is electrical potential energy per
charge.
22
Electric Potential
• If we push a single charge against an electric field,
we do a certain amount of work. If we push two
charges against the same field, we do twice as much
work.
• Two charges in the same location in an electric field
will have twice the electrical potential energy as
one; ten charges will have ten times the potential
energy.
• It is convenient when working with electricity to
consider the electrical potential energy per charge.
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Electric Potential
• The electrical potential energy per charge is the total
electrical potential energy divided by the amount of
charge.
• At any location the potential energy per charge—
whatever the amount of charge—will be the same.
• The concept of electrical potential energy per charge
has the name, electric potential (V).
𝑬𝒍𝒆𝒄𝒕𝒓𝒊𝒄𝒂𝒍 𝒑𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚
𝑬𝒍𝒆𝒄𝒕𝒓𝒊𝒄 𝒑𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍 =
𝒄𝒉𝒂𝒓𝒈𝒆
24
Electric Potential
• The Electric potential or VOLTAGE (V) is defined to be the
work (W) done by the electric force in transporting a unit of
positive charge (q) from one point to another.
V=W/q
Unit: volt (or) joule / coulomb
• Electric Potential Energy U is the energy of a charged
object in an external electric field (Unit Joule J)
• Electric Potential V (or Voltage) is electric potential
energy per unit charge, measured in joules per coulomb
(Unit Volt V)
25
Electric Potential due to Point
Charges
• The electric potential at a distance (r) away from a
point charge (Q) becomes
When more than one point charge is present, by
applying the superposition principle, the total electric
potential is simply the sum of potentials due to
individual charges:
26
Electric Potential due to
Collection of Point Charges
From the equation for the electric
potential of a point charge, we can
find the electric potential of an
arbitrary distribution of electric
charge by generalization.
If there are a number of individual
point charges in the system the potential at some
point in space, that we call the observation point, is
simply the algebraic sum of the individual potentials
due to each charge.
Where (ri) is the distance from the observation point to the charge,(qi).
27
Potential Energy in Two
Points of Charges
• If a system of charges is assembled by
an external agent, the next ΔU=
−W =+Wext. That is, the change in
potential energy of the system is
the work that must be put in by an
external agent to assemble the
Two point charges separated by a distance r
configuration.
A simple example is lifting a mass m
through a height h. The work done
by an external agent you, is (+mgh)
(The gravitational field does
work). The charges are brought in
from infinity without acceleration
i.e. they are at rest at the end of the
process.
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Potential Energy in Two
Points of Charges
• If q1 and q2 have the same sign, positive work must
be done to overcome the electrostatic repulsion and
the potential energy of the system is positive, U12>0
.
• On the other hand, if the signs are opposite, then
U12<0 due to the attractive force between the
charges.
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Potential Energy in a System of
Charges
• To add a third charge q3 to the
system the work required is
• The potential energy of this
configuration is then
A system of three point charges
• Generalizing to a system of
N charges
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Continuous Charge Distribution
• If the charge distribution
is continuous, the
potential at a point P can
be found by summing
over the contributions
from individual
differential elements of
charge dq.
Continuous charge distribution
31
Continuous Charge Distribution
• Taking infinity as our reference point with zero
potential, the electric potential at P due to dq is
• Summing over contributions from all
differential elements, we have
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Electric Potential
• Single point charge +Q
V = kq/r
(𝑘 =
1
4𝜋𝜀°
= 9 × 109 𝑁. 𝑚2 /𝐶 2 )
• Collection of point charges
V = Σkqi/ri
i=1,2,3,.....
• Continuous Charge
dV = kdq/r
33
Electric Potential
• An object of greater charge has more electrical
potential energy in the field of the charged
dome than an object of less charge, but the
electric potential of any charge at the same
location is the same.
34
Electric Potential
• The SI unit of measurement for electric potential is
the volt, named after the Italian
physicist Allesandro Volta.
• The symbol for volt is V.
• Potential energy is measured in joules and
charge is measured in coulombs,
𝑗𝑜𝑢𝑙𝑒
1 𝑣𝑜𝑙𝑡 = 1
𝑐𝑜𝑢𝑙𝑜𝑚𝑏
35
Potential Difference (voltage)
• The change in electric potential energy per charge is
known as potential difference or voltage and is
measured in Volt.
ΔV = ΔU/q0 = -W/q0
1V [Volt] =1 Nm/C
1 joule = 6.24150934×1018 electron volts (ev)
36
Electric Potential in a Uniform Field
• The work done by the electric
field to move a positive charge q
from A, (the positive plate
higher potential), to B,
(the negative plate, lower
Potential), is
W = −ΔU = − qΔV
• The potential difference between
points A and B is
−Δ V = −(VB − VA) = VA − VB = VAB
• Entering this in to the expression for work yields
W = qVAB
37
Electric Potential in a Uniform Field
• Work is W = Fd cos θ; here cos θ = 1, since the path
is parallel to the field,
and so W = Fd. Since F = qE,
we see that W = qEd. Substituting this expression for
work into the previous equation gives
qEd = qVAB.
The charge cancels, and so the voltage between
points A and B is seen to be
ΔV=Ed
38
The Van de Graaff Generator
• A common laboratory device for building
up high voltages is the Van de Graaff
generator.
• This is the lightning machine often used
by “evil scientists” in old science fiction
movies.
39
The Van de Graaff Generator
• In a Van de Graaff generator, a moving rubber
belt carries electrons from the voltage source
to a conducting sphere.
40
The Van de Graaff Generator
• A large hollow metal sphere is supported by a
cylindrical insulating stand.
• A rubber belt inside the support stand moves past
metal needles that are maintained at a high electric
potential.
• A continuous supply of electrons is deposited on the
belt through electric discharge by the points of the
needles.
• The electrons are carried up into the hollow metal
sphere.
41
The Van de Graaff Generator
• The electrons leak onto metal points attached
to the inner surface of the sphere.
• Because of mutual repulsion, the electrons
move to the outer surface of the conducting
sphere.
• This leaves the inside surface uncharged and
able to receive more electrons.
• The process is continuous, and the charge
builds up to a very high electric potential—on
the order of millions of volts.
42
The Van de Graaff Generator
• In modern times, the application of Van De Graff
generators is largely limited to academic purposes to
demonstrate the practical aspects and concepts of
electrostatic behavior of particles.
43
Questions
1-
2-
44
Questions
3. An electric field has
a. no direction.
b. only magnitude.
c. both magnitude and direction.
d. a uniformed strength throughout.
4. In the electric field surrounding a group of charged
particles, field strength is greater where field lines are
a. thickest.
b. longest.
c. farthest apart.
d. closest.
45
Questions
5. The potential energy of a compressed spring and the
potential energy of a charged object both depend
a. only on the work done on them.
b. only on their locations in their respective fields.
c. on their locations in their respective fields and on
the work done on them.
d. on their kinetic energies exceeding their potential
energies.
46
Questions
6. Electric potential is related to electrical potential
energy as
a. The two terms are different names for the same
concept.
b. electric potential is the ratio of electrical potential
energy per charge.
c. Both are measured using the units of coulomb.
d.Both are measured using only the units of joules.
47
Questions
1. A balloon rubbed against denim gains a charge of
−8.0 μC. What is the electric force between the
balloon and the denim when the two are separated
by a distance of 5.0 cm? (Assume that the charges
are located at a point.)
48
Questions
2- How strong is the electric field between two parallel
plates 5.2 mm apart if the potential difference between
them is 220V?
49
Questions
3- If there were twice as much charge on one of
the objects, would the electrical potential
energy be the same or would it be twice as
great?
50
Questions
4- How can the voltage of a Van de Graaff
generator be increased?
5- What is the potential energy of a 5 mC charge
placed at an electric potential of 1000 V?
6- Calculate the electric potential 15 cm from a
metal sphere whose radius is 5 cm and has a
negative charge of -2.5 mC.?
51
References
• College Physics,1st edition, by OpenStax College
• Physics (3rd Edition) by James S. Walker (Jan 29,
2006)
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