Transcript Static Electricity

2/3/15 do now – on a new sheet
• What are the particles and their charges in
an atom?
• Homework – castle learning
• Midterm Exam – part I – tomorrow – in
class
Static Electricity - Chapter Outline
Lesson 1: Basic Terminology and Concepts
Lesson 2: Methods of Charging
Lesson 3: Electric Force
Lesson 4: Electric Fields
Lesson 5: Electric Potential
Lesson 1: Basic Terminology
and Concepts
1.
2.
3.
4.
5.
6.
The Structure of Matter
Neutral vs. Charged Objects
Charge as a Quantity
Charge Interactions
Conductors and Insulators
Polarization and electroscope
The Structure of Matter
• ATOMS- All material objects are composed of
atoms.
• Atoms contain a dense center called the
nucleus and a larger surrounding of mostly
empty space that contains the electrons.
Summary of Subatomic
Particles
Nucleus
Proton
Electron
Neutron
Outside nucleus
Weakly Bound
Tightly Bound Tightly Bound
Neg. Charge
+ Charge
No Charge
Not very
Massive
Massive
massive
-27
-27
(1.67 X10 kg) (1.67X10 kg)
(9.11X10-31kg)
Can not be
Can not be
Can be added
added or
added or
or removed
removed
removed
easily
easily
easily
Neutral vs. Charged Objects
Charged objects contain unequal numbers of protons
and electrons
PositivelyCharged
NegativelyCharged
Uncharged
Possesses more
protons than
electrons
Possesses more
electrons than
protons
Equal numbers
of protons and
electrons
• Note: protons and neutrons can not be removed,
only electrons can be removed or Added!
example
•
1.
2.
3.
4.
Which part of an atom is most likely to be
transferred as a body acquires a static
electric charge?
proton
neutron
electron
positron
example
•
1.
2.
3.
4.
A glass rod is given a positive charge by
rubbing it with silk. The rod has become
positive by
gaining electrons
gaining protons
losing electrons
losing protons
Charge as a Quantity
• There are two ways to express the quantity of charge on
an object.
• ELEMENTARY CHARGE (e). This is the charge of an
electron or a proton. For example, if an object have +5.6
x 107 e, this means that the object has 5.6 x 107 more
protons than electrons.
• COULOMB (C). There are 6.25 x 1018 elementary charge
in 1 C of charge. For example, if an object’s charge is - 0.2
C, this means that the object has (0.2 x 6.25 x 1018) excess
electrons.
The relationship between Coulomb
and elementary charge
•
•
•
•
1C = 6.25 x 1018 e
1e = 1.6 x 10-19 C
The charge of 1 electron is -1e, or -1.60 x 10-19 C
The charge of 1 proton is +1e, or +1.60 x 10-19
• One Coulomb of charge is an abnormally large
quantity of charge. Smaller values such as µC and
nC are often used.
Possible charges on any object
• Since objects are charged through electron transfers, the
charged objects must have either excess of absence
whole number of electrons. It can not have a fraction of
an electron. For Example, an object may have an excess
of 501 electrons, but not 501.4 electrons. Or an object may
have an absence of 423 electrons, but not 423.2 electrons.
• An charged object can only have a charge that is multiple
of the elementary charge – multiple of 1.6 x 10-19 C.
• The smallest charge any object can have is 1.6 x 10-19 C
Example
• An object has three excess electrons.
– What is its “elementary charge”?
-3e
– What is its charge in coulombs?
q = -3e x (1.6 x 10-19 C)/e = -4.8 x 10-19 C
Example
• An object has 75 protons and 65 electrons
– What is its “elementary charge”?
+10 e
– What is its charge in coulombs?
q = +10e x (1.6 x 10-19 C)/e = +16 x 10-19 C
Example
An object can not have a charge of
1. 3.2 × 10-19 C
2. 4.5 × 10-19 C
3. 8.0 × 10-19 C
4. 9.6 × 10-19 C
Charge Interactions
• The electric force is a non-contact force. Any charged
object can exert this force upon other objects - both
charged and uncharged objects.
• Two simple and fundamental statements can be made
about the nature of the electric force.
• Opposites attract. likes repel.
The Electric Force and Newton's Third Law
This electric force exerted between two charged objects is a
force in the same sense that friction, tension, gravity and air
resistance are forces. And being a force, the same laws and
principles that describe any force describe the electrical
force. One of those laws was Newton's law of actionreaction. (balloons)
Force of B upon A is the same
in magnitude as Force of A
upon B. they are action and
reaction forces.
Force of D upon C is the same
in magnitude as Force of C
upon D. they are action and
reaction forces.
Interaction Between Charged and
Neutral Objects
• Any charged object - whether positively charged
or negatively charged - will have an attractive
interaction with a neutral object.
– Positively charged objects and neutral objects
attract each other;
– Negatively charged objects and neutral
objects attract each other.
• In accordance with Newton's law of actionreaction, the neutral object attracts the
charged object.
Charge detection
• If two objects repel each other, one can
conclude that both objects are charged and
charged with the same type of charge. One
could not conclude if they are both positively
charged or both negatively charged.
• If two objects attract each other, one can
conclude that at least one of the objects is
charged. The other object is either neutral or
charged with the opposite type of charge. You
cannot draw a conclusion about which one of
the objects is charged or what type of charge
(positive or negative) the charged object
possesses.
example
•
A lightweight sphere hangs by an insulating
thread. A student wishes to determine if the
sphere is neutral or electro statically charged.
She has a negatively charged hard rubber rod
and a positively charged glass rod. She does
not touch the sphere with the rods, but runs
tests by bringing them near the sphere one at
a time. The student notes that the sphere is
attracted to both rods. This test result shows
that the charge on the sphere is
1. positive
2. negative
3. neutral
example
•
1.
2.
3.
4.
A negatively charged plastic comb is
brought close to, but does not touch, a
small piece of paper. If the comb and the
paper are attracted to each other, the
charge on the paper
may be negative or neutral
may be positive or neutral
must be negative
must be positive
Midterm Exam Part I
• After you finish the midterm, you should
work on packets:
• Static electricity pp. #1-4
• Worksheet 4.1.1 #1-8
Please Recycle – the box is in front of the
classroom
2/5
• Static electricity pp. #1-4
• Worksheet 4.1.1 #1-8
Homework - Castle learning
2/6 do now
1. An object possessing an excess of 6.0 ×
106 electrons. What is net charge in
coulombs?
2. An object has 6.08 μC of negative
charge. How many excess electrons does
the object have?
Home work – castle learning
Total castle learning assignments for this unit 2
If there is a snow day on Monday – Worksheets
(packet) 3.2.1 – 3.2.5 are due Tuesday
Conductors and Insulators
• The behavior of a charged object depends on whether the
object is made of a conductive or a nonconductive
material.
• Conductors are materials that permit electrons to flow
freely from atom to atom and molecule to molecule.
• In contrast to conductors, insulators are materials that
impede the free flow of electrons from atom to atom
and molecule to molecule.
insulator
conductor
insulators
vs.
Charge on an insulator
will remain at the initial
location of charging.
conductors
Charge on a conductor is
quickly distributed across
the entire surface of the
object. This electron
migration happens across
the entire surface of the
object, until the overall sum
of repulsive affects
between electrons across
the whole surface of the
object are minimized.
Examples of conductors and insulators
• Examples of conductors include
– metals,
– aqueous solutions of salts
– graphite,
– water
– human body.
• Examples of insulators
– plastics,
– Styrofoam,
– paper,
– rubber,
– glass
– dry air.
The division of materials into the categories of conductors
and insulators is a somewhat artificial division. It is more
appropriate to think of materials as being placed somewhere
along a continuum.
Check your understanding
• Suppose that a conducting sphere is charged
positively by some method. The charge is
initially deposited on the left side of the sphere.
Yet because the object is conductive, the charge
spreads uniformly throughout the surface of the
sphere. The uniform distribution of charge is
explained by the fact that ____.
a. the charged atoms at the location of charge
move throughout the surface of the sphere
b. the excess protons move from the location of
charge to the rest of the sphere
c. excess electrons from the rest of the sphere are
attracted towards the excess protons
•
a.
b.
c.
d.
e.
f.
A conductor differs from an insulator in that a
conductor ________.
has an excess of protons
has an excess of electrons
can become charged and an insulator cannot
has faster moving molecules
does not have any neutrons to get in the way
of electron flow
none of these
Polarization and Electroscope
• The interaction between a neutral object and
any charged object can be explained using our
usual rules of opposites attract and likes
repel.
Polarization
• In an atom, the protons are tightly bound in a nucleus
and incapable of movement. In conducting objects,
electrons are so loosely bound that they may be
induced into moving from one portion of the object to
another portion of the object. By placing a charged
object near a neutral conducting object you can create
electron movement.
• Polarization is inducing movement of electrons
within an object by a charged body.
Polarization is not charging
• No electrons have been added to or subtracted during
polarization. The charges are simply separated to the
opposite ends of the object. The overall charge of the
object is electrically neutral.
Neutral
The Electroscope
• An electroscope is a device which is capable of detecting
the presence of a charges in an object through
polarization.
An Insulator can be Polarized
• In an insulator, electrons merely redistribute
themselves within the atom or molecules nearest the
outer surface of the object.
Polarization of water molecules
example
• An inflated balloon which has been rubbed against a
person's hair is touched to a neutral wall and remains
attracted to it. Which diagram best represents the
charge distribution on the balloon and the wall?
a
b
c
d
example
• The diagram below shows three neutral
metal spheres, x, y, and z, in contact and
on insulating stands. Which diagram best
represents the charge distribution on the
spheres when a positively charged rod is
brought near sphere x, but does not touch
it?
C
A
D
B
Lesson 2: Methods of Charging
1.
2.
3.
4.
5.
Charging by Friction
The Law of Conservation of Charge
Charging by Conduction
Charging by Induction
Grounding - the Removal of a Charge
Charging by Friction
• When two objects are rubbed together electrons may be
transferred from one object to another. One object gains
electrons and the other object loses electrons, so both
objects have a charge.
electron affinity
• The property of electron affinity refers to the
relative amount of love that a material has for
electrons. High affinity means the material has
more pull to electrons.
• The more love of electrons a material has the
more likely it is to steal electrons from the other
object during charging by friction.
Triboelectric series
• A triboelectric series is an
ordering of substances with
high affinities on top.
• When any two materials in the
table are rubbed together, the
one which is higher can be
expected to pull electrons from
the material which is lower.
Law of Conservation of Charge
• The total amount of charge in a closed
system remains constant – charge is not
created or destroyed, it only moves from one
object to another
• Charge “moves” as a result of ELECTRON
movement ONLY!!!
example
•
1.
2.
3.
4.
The diagram shows four charged metal
spheres suspended by strings. The charge of
each sphere is indicated. If spheres A, B, C,
and D simultaneously come into contact, the
net charge on the four spheres will be
+1 C
+2 C
+3 C
+4 C
example
•
a.
b.
c.
d.
During a physics lab, a plastic strip was rubbed with
cotton and became positively charged. The correct
explanation for why the plastic strip becomes positively
charged is that ...
the plastic strip acquired extra protons from the cotton.
the plastic strip acquired extra protons during the
charging process.
protons were created as the result of the charging
process.
the plastic strip lost electrons to the cotton during the
charging process.
Charging by Conduction
• Charging by conduction involves the contact of a
charged object to a neutral object.
• When charging by conduction both object have the
same type of charge when separated.
• To charge by conduction successfully, your charged and
neutral object must be conductors!
Law of Conservation of Charge
• In each of the methods of charging: - charging
by friction and charging by induction – and
charging by conduction, the law of conservation
of charge is observed. The law of conservation
of charge states that charge is always
conserved. The total amount of charge among
the objects is the same before the process starts
as it is after the process ends.
example
•
1.
2.
3.
4.
Two metal spheres having charges of
+4.0 × 10-6 coulomb and +2.0 × 10-5
coulomb, respectively, are brought into
contact and then separated. After
separation, the charge on each sphere is
8.0 × 10-11 C
8.0 × 10-6 C
2.1 × 10-6 C
1.2 × 10-5 C
example
• A physics student, standing on the ground, touches an
uncharged plastic baseball bat to a negatively charged
electroscope. This will cause ___.
a. the electroscope to be grounded as electrons flow out of
the electroscope.
b. the electroscope to be grounded as electrons flow into
the electroscope.
c. the electroscope to be grounded as protons flow out of
the electroscope.
d. the electroscope to be grounded as protons flow into the
electroscope.
e. the baseball bat to acquire an excess of protons.
f. absolutely nothing (or very little) to happen since the
plastic bat does not conduct.
2/9 do now
1. An object possessing an excess of 3.0 ×
103 electrons. What is net charge in
coulombs?
2. An object has 5.08 nC of negative
charge. How many excess electrons does
the object have?
Home work – castle learning
Charging by Induction
• charging by induction method is to charge an object
without actually touching the object to any other
charged object.
Charging by induction using negatively charged object
Charging by induction using positively charged object
The law of conservation of charge is easily observed in the
induction charging process. The overall charge on the
system of two objects is the same after the charging process
as it was before the charging process
Charging a single sphere by
induction
The Importance of a Ground in
Induction Charging
• In the charging by induction cases, charge is
never transferred from the charged object to
the neutral object… They do not touch!
• The charged object causes the neutral object to
become polarized.
• The object that touches the now polarized object
serves as a supplier or receiver of electrons.
This electron source and receiver is known as a
ground.
Grounding - the Removal of a
Charge
• Grounding is a way of uncharging an object. It is the
process of removing the excess charge on an object by
means of the transfer of electrons between it and another
object of substantial size. When a charged object is
grounded, the excess charge is balanced by the transfer
of electrons between the charged object and a ground.
• A ground is simply an object that serves as a seemingly
infinite reservoir of electrons; the ground is capable of
providing electrons to or receiving electrons from a
charged object in order to neutralize that object.
• Any object can be grounded provided that the charged
atoms of that object have a conducting pathway
between the atoms and the ground.
A ground is simply a large object that serves as
an almost infinite source or sink of electrons.
Check Your Understanding
• A positively charged pop can is touched by a
person standing on the ground. The pop can
subsequently becomes neutral. The pop can
becomes neutral during this process because
______.
a. electrons pass from the pop can to the person
(ground)
b. electrons pass from the person (ground) to the
pop can
c. protons pass from the pop can to the person
(ground)
d. protons pass from the person (ground) to the
pop can
If grounding removes charge how does it aid
in charging an object during induction?
•When the object is polarized, one side has a positive charge
and the other has a negative charge.
•The ground is removing the excess electrons on the sphere
on one side but it can’t remove the positive charges because
these charges are being balanced by the negative charged
balloon that is near the sphere.
Charging an electroscope by
induction
1. Bring a charged object near the
electroscope
2. The electroscope is being
polarized.
3. Touch the part of the
electroscope that is away from
the charged object.
4. Remove your hand.
5. Remove the charged object.
fundamental principles regarding
induction charging
1. The charged object never touches to the object being
charged by induction.
2. The charged object does not transfer electrons to or
receive electrons from the object being charged.
3. The charged object serves to polarize the object being
charged.
4. The object being charged is touched by a ground;
electrons are transferred between the ground and the
object being charged (either into the object or out of it).
5. The object being charged ultimately receives a charge
that is opposite that of the charged object which is used
to polarize it.
example
•
1.
2.
3.
4.
A charged body may cause the
temporary redistribution of charge on
another body without coming in contact
with it. This process is called
conduction
potential
Charging by friction
induction
Class work
• Electricity packet – pp. 5-12
• Worksheet 4.1.2 Transfer of Charges
Lesson 3: Electric Force
1.
2.
3.
4.
Charge Interactions Revisited
Coulomb's Law
Inverse Square Law
Electrical Force and Newton's Laws
Charge Interactions Revisited
• The two fundamental charge interactions are:
– oppositely charged objects attract
– like charged objects repel.
• These mutual interactions resulted in an electrical force
between the two charged objects.
The electrical forces, like all forces,
are vector quantity.
The electrical force is a non-contact
force - it exists despite the fact that
the interacting objects are not in
physical contact with each other.
example
• An electron is located 1.0 meter from a
+2.0-coulomb charge, as shown in the
diagram. The electrostatic force acting on
the electron is directed toward point
A
1. A
2. B
D
3. C
B
4. D
C
example
• Two plastic rods, A and
B, each possess a net
negative charge of 1.0 ×
10-3 coulomb. The rods
and a positively charged
sphere are positioned as
shown in the
diagram. Which vector
below best represents the
resultant electrostatic
force on the sphere?
a
b
c
d
Coulomb's Law
• The interaction between charged objects is a noncontact force that acts over some distance of
separation. The force between two charged objects
depends on three variables:
charge
– The ______________on
object 1, (q1)
– The ______________
on object 2, (q2)
charge
– The _________________
between them. (r)
distance
kq1q2
Fe  2
r
q1
r
•k is a proportionality constant known as the Coulomb's law
constant. k = 8.99 x 109 N • m2 / C2.
•Fe: force between two charges, (in Newtons)
q2
kq1q2
Fe  2
r
• Coulomb's law states that the electrical force between two
charged objects is directly proportional to the product of the
quantity of charge on the objects and inversely proportional
to the square of the separation distance between the two
objects.
• The force value is positive (repulsive) when q1 and q2 are of
like charge - either both "+" or both "-".
• The force value is negative (attractive) when q1 and q2 are of
opposite charge - one is "+" and the other is "-".
Example
• Two balloons with charges of +3.37 µC and -8.21 µC
attract each other with a force of 0.0626 Newtons.
Determine the separation distance between the two
balloons.
Given:
Find: d = ?
q1 = +3.37 µC = +3.37 x 10-6 C
q2 = -8.21 µC = -8.21 x 10-6 C
Fe = -0.0626 N (negative sign indicate attractive force)
k  q1  q2
Fe 
2
r
r2 • Fe = k • q1 • q2
r2 = k • q1 • q2 / Fe
r = √(k • q1 • q2 / Fe
r = +1.99 m
Example
• Suppose that two point charges, each with a charge of
+1.00 Coulomb are separated by a distance of 1.00
meter. Determine the magnitude of the electrical force of
repulsion between them.
Given:
Fe = k • q1 • q2 / d2
q1 = 1.00 C
Fe = (8.99 x 109 N•m2/C2) • (1.00 C) •
q2 = 1.00 C
(1.00 C) / (1.00 m)2
r = 1.00 m
Find: Fe =?
Fe = 9.0 x 109 N
This is an incredibly large force which compares in magnitude to
the weight of more than 2000 jetliners.
Objects simply do not acquire charges on the order of 1.00
Coulomb. In fact, Charge is often expressed in units of
microCoulomb (µC) and nanoCoulomb (nC).
1 C = 106 μC
1 C = 109 nC
Electrical vs. Gravitational Forces
Fe 
k  q1  q2
r2
k = 8.99 x 109 N·m2/C2
The similarities:
Both equations have same form.
Both equations show an inverse
square relationship between
force and separation distance.
both equations show that the
force is proportional to the
product of the quantity that
causes the force.
Both electrical force and
gravitational force are noncontact forces.
G  m1  m2
Fe 
r2
G = 6.67 x 10-11 N·m2/kg2
The difference:
Coulomb's law constant (k) is
significantly greater than
Newton's universal gravitation
constant (G). Subsequently the
force between charges –
electric force - are significantly
stronger than the force
between masses – gravitational
force.
Gravitational forces are only
attractive; electrical forces can
be either attractive or
repulsive.
example
• The diagram below shows two identical metal spheres, A and
B, separated by distance d. Each sphere has mass m and
possesses charge q.
•
• Which diagram best represents the electrostatic force Fe and
the gravitational force Fg acting on sphere B due to sphere
A?
A
B
C
D
example
• Two protons are located one meter apart.
Compared to the gravitational force of
attraction between the two protons, the
electrostatic force between the protons is
1.stronger and repulsive
2.weaker and repulsive
3.stronger and attractive
4.weaker and attractive
Coulomb’s Law – force and distance have
inverse squared relationship
k  q1  q2
Fe 
r2
F
d
• That is, the factor by which the electrostatic force is
changed is the inverse of the square of the factor by
which the separation distance is changed.
• If the separation distance is doubled (increased by a
factor of 2), then the electrostatic force is decreased by
a factor of four (22)
• If the separation distance is tripled (increased by a
factor of 3), then the electrostatic force is decreased by
a factor of nine (32).
example
•
1.
2.
3.
4.
Two charges that are 2 meters apart
repel each other with a force of 2x10 -5
newton. If the distance between the
charges is decreased to 1 meter, the
force of repulsion will be
1 x 10-5 N
5 x 10-6 N
8 x 10-5 N
4 x 10-5 N
example
•
1.
2.
3.
4.
If the charge on each of two small
spheres a fixed distance apart is
doubled, the force of attraction between
the spheres will be
quartered
doubled
halved
quadrupled
example
• Which graph best represents the electrostatic force
between an alpha particle with a charge of +2
elementary charges and a positively charged nucleus as
a function of their distance of separation?
A
B
C
D
Coulomb’s law – force and charge have
direct relationship
k  q1  q2
Fe 
2
r
• Electrostatic force is directly
proportional to the charge of each
object. So if the charge of one object is
doubled, then the force will become two
times greater. If the charge of each of
the object is doubled, then the force will
become four times greater.
example
• A repulsive electrostatic force of magnitude F
exists between two metal spheres having
identical charge q. The distance between their
two centers is r. Which combination of changes
would produce no change in the electrostatic
force between the two spheres?
1. doubling q on one sphere while doubling r
2. doubling q on both spheres while doubling r
3. doubling q on one sphere while halving r
4. doubling q on both spheres while halving r
Electrical Force and Newton's Laws
• Electric force, like any force, is analyzed by Newton's
laws of motion.
• The analysis usually begins with the construction of a
free-body diagram. The magnitudes of the forces are
then added as vectors in order to determine the
resultant sum, also known as the net force. The net force
can then be used to determine the acceleration of the
object.
• In some instances, the free-body diagram is used to
determine the spatial separation or charge of two
objects that are at static equilibrium. In this case, the
free-body diagram is combined with an understanding of
vector principles in order to determine some unknown
quantity.
example
• A 0.90x10-4 kg balloon with a charge of -7.5 x 10-10 C is
located a distance of 0.12 m above a plastic golf tube which
has a charge of -8.3 x 10-10 C. Determine the acceleration of
the balloon at this instant?
free body diagram
find individual forces and Fnet & a
Fgrav = m•g = (0.90x10-4 kg)•(9.81 m/s2)
Fgrav = 8.82 x 10-4 N, down
Felect = k • q1 • q2 /r2
Felect= (8.99x109 N•m2/C2)•(-75 x 10-9 C)•(-83 x 10-9 C) / (0.12m)2
Felect = 3.89 x 10-7 N, up
Fnet = Fgrav (down) + Felect (up)
Fnet = - 8.82 x 10-4 N + 3.89 x 10-7 N
Fnet = - 8.82 x 10-4 N, down
a = Fnet / m
a = (8.82 x 10-4 N/ (0.90x10-4 kg )
a = 9.8 m/s2, down
example
• Balloon A and Balloon B are charged in a like manner by
rubbing with animal fur. Each acquires 4.0 x 10-6 C. If the
mass of each balloon is 1 gram, then how far below
Balloon B must Balloon A be held in order to levitate
Balloon B at rest? Assume the balloons act as point
charges.
Felec
Fg=m•g= 0.0098 N.
Fg
Fe=m•g= 0.0098 N.
Fe = k•q1•q2 / r2
r = √ k(q1• q2) / Fe
r = 3.83 meters
Lesson 4: Electric Fields
1. Electric force and gravitational force
are field force
2. Electric field and Gravitational Field
Concept
3. Electric Field Intensity (magnitude and
direction)
4. Electric Field Lines
5. Electric Fields and Conductors
6. Lightning
Electric force and gravitational force
are field forces
Gravitational force - the
mass of the Earth exerted an
influence, affecting other
masses which were in the
surrounding neighborhood.
electrical force – The
charges exerts an influence over
a distance affecting other
charges which were in the
surrounding neighborhood
Electric Field and Gravitational Field
Concept
• How can an apple reach across
space and falls toward Earth?
• The massive Earth creates a
Gravitational field. Other masses in
that field would feel its effect in the
space. Whether a massive object
enters that space or not, the
gravitational field exists.
• Similarly, a charged object
creates an electric field. Other
charges in that field would feel its
effect in the space. Whether a
charged object enters that space
or not, the electric field exists.
Electric and gravitational Field
Gravitational field
strength
• Force per mass ratio
g = Fg / m
• Direction is toward center
of Earth
Electric field strength
• Force per charge ratio
E = Fe / q
• The direction of the electric
field vector is the direction
that a positive test charge
is pushed or pulled when in
the presence of the electric
field.
Electric Field Strength
(magnitude)
Fe
E
q
kQq
( 2 )
kQ
d
E
 2
q
d
• Electric field strength (E) is the force per charge ratio. The unit for
electric field is N/C
• q is the charge in the field (test charge) – in Coulombs
• Fe is the force on the test charge q – in Newton
• k: constant, k = 8.99 x 109 Nm9/C2
• Q: source charge – in Coulombs
• d: distance from the source charge - in m
e
kQ
E 2
d
• Note that there are two charges here - the source
charge and the test charge. Electric field is the force per
quantity of charge on the test charge.
• The electric field strength is not dependent upon the
quantity of charge on the test charge.
• The electric field strength is dependent upon the quantity
of charge on the source charge Q and the distance of
separation d from the source charge. Just like the
gravitational field does not depends how much you
weigh!
An Inverse Square Law
• Electric field strength is location dependent, and its
magnitude decreases as the distance from a location to
the source increases. And by whatever factor the
distance is changed, the electric field strength will
change inversely by the square of that factor.
E
k∙Q
E=
d2
d
example
• What is the magnitude of the electric force
acting on an electron located in an electric
field with an intensity of 5.0 x 103 N/C?
E = 5.0 x 103 N/C
q = 1.6 x 10-19 C
F =? N
E = F/q
F = Eq
F = (5.0 N x 103 N/C) x (1.6 x 10-19 C)
= 8.0 x 10-16 N
example
• What is the magnitude of an electrostatic
force experienced by one elementary
charge at a point in an electric field where
the electric field intensity is 3.0 × 103 N/C?
E = 3.0 x 103 N/C
q = 1.6 x 10-19 C
F =? N
E = F/q
F = Eq
F = (3.0 N x 103 N/C) x (1.6 x 10-19 C)
= 4.8 x 10-16 N
example
• The diagram above represents a
uniformly charged rod. Which graph
below best represents the relationship
between the magnitude of the electric
field intensity (E) and the distance from
the rod as measured along line AB?
A
B
C
D
example
•
Suppose that two equally charged spheres
attract each other with a force of -0.5 N ("-"
means attractive) when placed a distance of
30. cm from each other. Determine the charge
of the spheres. PSYW
The Direction of the Electric Field Vector
• Electric field strength is a _______quantity.
vector
• the direction of the electric field vector is defined as the
positive test charge
direction that a ______________________________
is
pushed or pulled when in the presence of the electric
field.
• the electric field vector would always be directed
_______
away from positively-charged objects.
towards
• electric field vectors are always directed ____________
negatively-charged objects
Electric Field Maps
+
-
Electric Field Maps
+
+
Electric Field Maps
+-
+-
Rules for Drawing Electric Field Patterns
1.
2.
The lines must begin on positive charges and
terminate on negative charges
Surround more charged objects by more lines.
The electric field is greatest at locations closest to the
surface of the charge and least at locations further from the
surface of the charge.
3.
draw the lines of force ___________________
to the
perpendicular
surfaces of objects at the locations where the lines
connect to object's surfaces.
4.
never cross
Electric field lines should _____________________.
• Examples of electric field lines
example
•
1.
2.
3.
4.
The diagram shows the electric field in the vicinity of
two charged conducting spheres, A and B. What is the
static electric charge on each of the conducting
spheres?
A is negative and B is positive.
A is positive and B is negative.
Both A and B are positive.
Both A and B are negative.
example
• Two small metallic spheres, A and B, are separated by a
distance of 4.0 × 10-1 meter, as shown. The charge on each
sphere is +1.0 × 10-6 coulomb. Point P is located near the
spheres. Which arrow best represents the direction of the
resultant electric field at point P due to the charges on spheres
A and B?
1
2
3
4
Fields between two oppositely charged
parallel plates
• If the distance separating
two oppositely charged
parallel plates is small
compared to their area, the
electric field between the
plates is ____________.
uniform
• The field lines are from
positive plate to the
negative plate.
force is the same
• Since F = E∙q, the __________________________
on a
charged particle anywhere inside the plates.
• A charged particle will accelerate toward the plate with the
opposite charge.
++++++++++++++++++++++++++++++++++++++++++++++
┼
─
example
•
As an electron moves
between two charged
parallel plates from point B
to point A, as shown in the
diagram, the force of the
electric field on the electron
1. decreases
2. increases
3. remains the same
example
•
1.
2.
3.
4.
In the diagram, proton p, neutron n, and electron e are
located as shown between two oppositely charged
plates. The magnitude of acceleration will be greatest
for the
neutron, because it has the greatest mass
neutron, because it is neutral
electron, because it has the smallest mass
proton, because it is farthest from the negative plate
Millikan’s oil-drop experiment
• In 1909, Robert Millikan performed the oil-drop
experiment to measure the elementary electric charge.
The experiment entailed balancing the downward
gravitational force with the upward electric forces on
tiny charged droplets of oil suspended between two metal
plates.
Fe
Fg
Fg = Fe
m∙g = E∙q
q = mg / E
• Milliken measured the forces on charged oil drops in a
uniform electric field.
• He found no drop with a charge less than 1.60 x 10-19
coulomb. The charges on other drops were integral
multiples of this value.
fundamental
• This finding demonstrated that there is a ______________
unit of charge. This elementary charge of 1.60 x 10-19
coulomb is called the charge on a single electron.
example
•
What did Milliken conclude after performing his
oil-drop experiment?
1. The charge on an electron is 1.0 C.
2. The mass of an electron is 1.7 × 10-27 kg.
3. The charge on any oil drop is an integral
multiple of the charge on an electron.
4. The charge on an oil drop may have any value
larger than 1.6 × 10-19 C.
example
• The diagram, which illustrates the Milliken oil drop
experiment, shows a 3.2 × 10-14-kilogram oil drop with a
charge of -1.6 × 10-18 coulomb. The oil drop was in
equilibrium when the upward electrical force on the drop
was equal in magnitude to the gravitational force on the
drop. What was the magnitude of the electric field
intensity when this oil drop was in equilibrium?
Fnet = Fe - Fg = 0
Fe = Fg
E∙q = m∙g
E(-1.6x10-18C) = 3.2x10-14kg(9.81 N/kg)
E = 1.96 x 105 N/C = -2.0 x 105 N/C
example
• An object with a net charge of 4.80 × 10-6 coulomb
experiences an electrostatic force having a magnitude of
6.00 × 10-2 newtons when placed near a negatively
charged metal sphere. What is the magnitude and
direction of electric field strength at this location? [show
all work including substitution with units]
Given: q = 4.8 x 10-6 C
F = 6.00 x 10-2 N
Unknown: E = ? N/C
Solve: E = F / q = 6.00 x 10-2 N / 4.0 x 10-6 C
E = 1.25 x 104 N/C directed toward the sphere.
Electric field and conductors
conductor
• A _______________
is material which allows electrons
to move relatively freely from atom to atom.
• Electrostatic equilibrium is the condition established
by charged conductors in which the excess charge has
optimally distanced itself so as to reduce the total
amount of repulsive forces. Once a charged conductor
has reached the state of electrostatic equilibrium, there
is no further motion of charge about the surface.
-
+
+
+
+
-
-
Four properties of conductor in electric
equilibrium
1.
The electric field anywhere beneath the surface of a
zero.
charged conductor is ___________.
•
This principle of shielding is commonly utilized today
as we protect delicate electrical equipment by
enclosing them in metal cases.
2.
Any excess charge on an isolated conductor resides
outer surface
entirely on the conductor’s ____________________.
3.
The electric field upon the surface of the conductor is
perpendicular to the surface.
directed entirely _________________
4.
The electric fields are strongest at locations along the
surface where the object is
most curved
______________________________.
example
•
1.
2.
3.
4.
A metallic sphere is positively charged.
The field at the center of the sphere due
to this positive charge is
positive
negative
zero
dependent on the magnitude of the
charge
Lightning
• Perhaps the most
known and powerful
displays of
electrostatics in nature
is a lightning storm.
• What is the cause and
mechanism associated
with lightning strikes?
• How do lightning rods
serve to protect
buildings from the
devastating affects of a
lightning strike?
Static Charge Buildup in the Clouds
• The precursor of any lightning
strike is the polarization of
positive and negative charges
within a storm cloud. The tops
of the storm clouds are known
to acquire an excess of
positive charge and the bottom
of the storm clouds acquire an
excess of negative charge.
• When a thunderhead passes over
the ground, electrons on Earth's
outer surface are repelled by the
negatively charged cloud's bottom
surface. This creates an opposite
charge on the Earth's surface.
Buildings, trees and even people
can experience a buildup of static
charge as electrons are repelled
by the cloud's bottom.
• The electric field between the
cloud and the Earth is similar to
the electric field between two
oppositely charged plates.
• When the difference in
negative and positive charges
between ground and cloud gets
large enough, a lightning bolt
begins. The excess electrons
on the bottom of the cloud start
a journey through the
conducting air to the ground at
speeds up to 60 miles per
second.
• As electrons travel close to the
Earth, it encounters the
positive charges traveling
upward, when the two types of
charges meet, lightning begins.
• The enormous and rapid flow of charge along this pathway
between the cloud and Earth heats the surrounding air,
causing it to expand violently. The expansion of the air
creates a shockwave which we observe as thunder
Lightning Rods and Other
Protective Measures
• Tall buildings, farm houses
and other structures
susceptible to lightning strikes
are often equipped with
lightning rods.
• the lightning rod serves to
safely divert the lightning to
the ground in event that the
cloud discharge its lightning
via a bolt.
Check Your Understanding
1. TRUE or FALSE:
The presence of lightning rods on top of
buildings prevents a cloud with a static charge
buildup from releasing its charge to the building.
2. TRUE or FALSE:
If you place a lightning rod on top of your home
but failed to ground it, then it is unlikely that your
home would be struck by lightning.
Lesson 5: Electric Potential
Difference
1. Electric Field and the Movement of Charge
2. Electric Potential Energy
3. Electric Potential Difference
Electric Field and the Movement of
Charge
• A charged object creates an electric field. Electric field
is a vector quantity. As another charged object enters
into the field, its movement is affected by the field.
Electric Potential Energy
• Electric potential energy are similar to gravitational potential energy both involve field forces.
Gravitational potential
energy is a result of
interaction between masses.
It depends on the mass and
the field strength and the
relative position.
PEg = mg∆h
Similarly, electric potential
energy is a result of
interaction between
charges. It depends on the
charge and field strength
and relative position.
-
High PE
Work done by
electric field
High PE
Work done by
external force
Low PE
-
Low PE
++++++++++++
Change Electrical Potential Energy
To increase PE
+
+
-
+
-
+
To decrease PE
+
+
example
++++++++++++++++++++++++++++++
A
+e B
As a positive charge moves for B to A, it potential energy is
_____.
a. increased
b. decreased
c. stays the same
Energy is conserved
• Electric energy can be produce from many sources and also
can be converted into other types of energy. Electric
potential energy is a form of mechanical energy:
TME = KE + PEg + PEs + PEe
+
+
+
+
d
-
• In a uniform field, when a charge is released, work done by
the field on the charge equals to its lose PE e and it gain in
KE because there is no friction.
1 2
W  F  d  q  E  d  PEe  KE  mv
2
The Gravitational Potential
GPE = mg∆h
g∆h, is a quantity that could be used
to rate various locations about the
surface of the planet in terms of
how much potential energy each
kilogram of mass would possess
when placed there.
g∆h, is known as gravitational potential.
GPE
gh 
m
Gravitational potential is defined as the PE/mass. It is mass
independent. Gravitational potential describes the affects of a
gravitational field upon objects that are placed at various locations
within it.
• Electric potential (V) is defined as potential energy per
charge.
• Electric potential is a property of the
PEe
location within an electric field. Electric
V
potential (V) does not depend on q.
q
The electric potential is
the same for all charges
at a given location. A
test charge with twice the
quantity of charge would
possess twice the
potential energy at that
location.
Equipotential lines
• Equipotential lines connect positions of equipotential
energy. As a charge moves on an equipotential line,
there is _________________in
potential energy. As
no change
the charge crosses equipotential lines, the potential
energy changes.
++++++++++++++++++++++++++++++
+e
+e
------------------------------------------------------
Electric Potential Difference
• Electric potential difference between point A and point B is the
change is potential between point A and B
PEB PEA W
V  VB  VA 


q
q
q
B
+e
A
W
V 
q
The standard metric unit on electric potential difference is the
volt or voltage. 1 Volt = 1 Joule / Coulomb.
If 1 joule of work is needed to move 1 C of charge from point A to
point B, the potential difference between point A & B is 1 Volt.
If 3 joule of work is needed to move 1 C of charge from point A to
point B, the potential difference between point A & B is 3 Volts
Electric Potential Energy - 2 units
W
V 
q
W  q  V
If 1 C of charge is moved across 1 V of potential difference, 1 Joule
of work/energy is needed.
If 1 e of charge is moved across 1 V of potential difference, 1 eV
(electron-volt) of work/energy is needed.
Both Joule and eV are units of electric energy.
Since 1 e = 1.6 x 10-19 C
1 eV = 1.60 x 10-19 J
Example #1
• 6.0 joules of work are done in pushing an object with
+3.0 coulombs of charge toward a charged plate.
– What type of charge does the plate have on it?
– How much potential energy was stored in the electric fields?
– How much electrical potential was generated?
Positive
6.0 J
V = W/q
V = 6.0 J / 3.0 C
V = 2.0 V
Example #2
• An object with a 2.0 coulomb charge is accelerated
through a potential difference of 10 volts.
– How much kinetic energy does the object gain?
V = W/q
W = Vq
W = (10 V)(2.0 C) = 20 J
Electron-volts
• Alternate unit for work/energy:
• Raises 1e to an electrical potential of 1 V
• 1 eV = 1.6 x 10-19 J
What is
is the
the energy
energy needed
needed to
to raise
raise four
two
What
electronsto
toaapotential
potentialof
of2.5
1.0volts?
volt?
electrons
V = W /q
1.0 V = W / 4e
2.5
2e
W = 2.0eV
10 eV
Example #3
• An electron travels a distance of 2.0 x 10-3 meter as its
electrical potential is raised by 300 volts.
– How much work is done on the electron?
V = W/q
V = W/q
300 V = W / 1e
300 V = W / 1.6 x 10-19 C
W = 300 eV
W = 4.8 x 10-17 J
Electric Potential in Circuits
A battery powered electric circuit has locations of high and low
potential.
Within the cells of the battery, the electric field is directed from the
positive terminal towards the negative terminal. As a positive test
charge move through the cells from the negative terminal to the
positive terminal, it would require work, thus the potential energy
of the charge would increase. It is for this reason that the positive
terminal is described as the high potential terminal.
• As a positive charge move through the wires from
the positive terminal to the negative terminal, it
would move in the direction of the electric field and
would not require work. The charge would lose
potential energy. The negative terminal is described
as the low potential terminal.
example
• How many eV is required to move 3.2 x 10-19 C
of charge through a potential difference of 5.0
volts?
V=W/q
5.0 V = W / (3.2 x 10-19 C) = W / (2 elem. Charges)
W = 10 eV
Example
•
Moving +2.0 coulombs of charge from infinity
to point P in an electric field requires 8.0 joules
of work. What is the electric field potential at
point P?
The electric potential at any point in an electric field is
the work required to bring a unit positive charge from
infinity to that point.
V = W / q = 8.0 J / (2.0 C) = 4.0 V
Example
• The graph shows the relationship between
the work done on a charged body in an
electric field and the net charge on the
body. What does the slope of this graph
represent?
Slope = rise / run
Slope = W / q = V
The slope represent the
potential difference.