Download Static Electricity

Static Electricity - Chapter Outline
Lesson 1: Basic Terminology and Concepts
The Structure of Matter
Neutral vs. Charged Objects
Charge Interactions
Conductors and Insulators
Polarization
Lesson 2: Methods of Charging
Charging by Friction
Charging by Conduction
Charging by Induction
Grounding
Lesson 3: Electric Force
Charge Interactions Revisited
Coulomb's Law
Inverse Square Law
Newton's Laws and the Electrical Force
Lesson 4: Electric Fields
Action-at-a-Distance
Electric Field Lines
Lightning
Electric Field Intensity
Electric Fields and Conductors
Lesson 5: Electric Potential
Electric Field and the Movement of Charge
Electric Potential
Electric Potential Difference
objectives
• Know:
– Charge is quantized.
– Charge on an electron and proton.
– Unit of charge.
• Understand:
– Relationship between fundamental charge and
charge in coulombs.
– Law of Conservation of Charge.
• Be able to:
– Convert from fundamental charges to coulombs
– Determine the charge on two or more objects after
they come in contact with one another.
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.
Electrons
• Electrons are present in the region of space
outside the nucleus. They are negatively
charged and weakly bound to the atom.
Electrons are often removed from and added to
an atom by normal everyday occurrences.
These occurrences are the focus of this Static
Electricity unit.
Protons and Neutrons
• The nucleus of the atom contains positively
charged protons and neutral neutrons. These
protons and neutrons are not removable by
usual everyday methods. It would require some
form of high-energy nuclear occurrence to
disturb the nucleus. Protons and neutrons will
remain within the nucleus of the atom.
• Electrostatic phenomenon can never be
explained by the movement of protons.
Summary of Subatomic
Particles
Nucleus
Proton
Electron
Neutron
Tightly Bound Tightly Bound
+ Charge
No Charge
Massive
Massive
(1.67 X10-27 kg) (1.67X10-27kg)
Outside nucleus
Weakly Bound
- Charge
Not very
massive
(9.11X10-31kg)
Check Your Understanding
•
a.
b.
c.
d.
e.
f.
____ are the charged parts of an atom.
Only electrons
Only protons
Neutrons only
Electrons and neutrons
Electrons and protons
Protons and neutrons
Charged versus Uncharged Objects
• Electrically charged objects are formed when neutral
objects lose or gain electrons.
• Note: protons and neutrons can not be removed, only
electrons can be removed or Added!
PositivelyCharged
NegativelyCharged
Uncharged
Possesses more
protons than
electrons
Possesses more
electrons than
protons
Equal numbers
of protons and
electrons
Charged objects contain unequal numbers of protons
and electrons
Charged Objects as an Imbalance of
Protons and Electrons
Negatively charged
Positively charged
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
Charge as a Quantity
• Like mass, the charge of an object is a measurable
quantity. The charge possessed by an object is often
expressed using the scientific unit known as the
Coulomb (C).
• One Coulomb of charge is an abnormally large quantity
of charge.
– An object with -1 C of charge would need an excess
of 6.25 x 1018 electrons,
– an object with a shortage of 6.25 x 1018 electrons
would have a total charge of +1 C.
• The units of micro-Coulombs (1 µC = 10-6 C) or nanoCoulombs (nC = 10-9 C) are more commonly used as the
unit of measurement of charge.
• +1.6 x 10 -19 Coulomb is called an elementary charge.
• The charge of one electron = -1e = -1.6 x 10 -19 C.
• The charge on a single proton = + 1e = +1.6 x 10 -19C.
• If an object is charged, it possesses more or less
whole numbers
____________________________of
electrons. It can not
possess a fraction of an electron. An object can only have a
charge that is multiple of the elementary charge –
multiple
______________of
1.6 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
example
•
1.
2.
3.
4.
What is the smallest electric charge that
can be put on an object?
9.11 × 10-31 C
1.60 × 10-19 C
9.00 × 109 C
6.25 × 1018 C
Determine the total charge of a
charged object
•
Determine the difference between the number of electrons
and the number of protons to find the excess charge.
– if there are less electrons,
the total charge = the number of excess charge x (+1.6x10-19 C)
– if there are more electrons,
the total charge = the number of excess charge x (-1.6x10-19 C)
•
Similarly, if the net charge is given, one can divide the net
charge by the elementary charge (1.6x10-19 C) to determine
the excess number of electrons or protons.
example
•
1.
2.
3.
4.
An object possessing an excess of 6.0 ×
106 electrons has a net charge of
2.7 × 10-26 C
5.5 × 10-24 C
3.8 × 10-13 C
9.6 × 10-13 C
example
•
1.
2.
3.
4.
Which quantity of excess electric charge
could be found on an object?
0.25 elementary charges
5.25 × 10-19 C
6.40 × 10-19 C
1.60 elementary charges
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.
objectives
• Know:
– Definition of insulator, conductor
– Charge is transferred in solids by electron movement only.
• Understand:
- How charges interact with each other
- How to detect charges
- How charges flow during polarization events.
• Be able to:
- Explain how charged object attract neutral objects
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.
The nature of the electric force:
1. Opposites attract.
2. 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.
• Any charged object - plastic, rubber, or
aluminum - will exert an attractive force upon a
neutral object. And in accordance with Newton's
law of action-reaction, 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 that the balloons 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
Conductors and Insulators
• The behavior of an object that has been charged
is dependent upon 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.
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.
Human body is a conductor
• Along the continuum of conductors and insulators,
one might find the human body somewhere
towards the conducting side of the middle. When
the body acquires a static charge it has a
tendency to distribute that charge throughout the
surface of the body.
• phet
Water is a conductor
• Water, being a conductor, has a tendency to gradually
remove excess charge from objects. Since humidity levels
tend to vary from day to day and season to season, it is
expected that electrical affects (and even the success of
electrostatic demonstrations) can vary from day to day.
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. Why do think this
happens?
The insulating cups are use to prevent charge from escaping
to the surroundings as well as to provide for a convenient
handle.
Distribution of Charge via Electron
Movement
• Predicting the direction that electrons would move within
a conducting material is a simple application of the two
fundamental rules of charge interaction. Opposites
attract and likes repel.
• The excess negative charge distributes itself throughout
the surface of the conductor. This is because electrons
wish to manipulate their surroundings in an effort to
reduce repulsive affects.
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
objectives
• Know:
– Definitions polarization and electroscope.
– Charge is transferred in solids by electron movement only.
• Understand:
- How charges flow during polarization events.
• Be able to:
– Draw and interpret pith ball and electroscope diagrams.
Polarization - Why a charged object
attract neutral object
• 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.
• No electrons have been added to or subtracted
from the can yet there is a charge at either end of
the can; overall the can is electrically neutral.
This arrangement of charge is called polarization.
• Polarization is the process of separating
opposite charges within an object.
• The polarization process always involves the
use of a charged object to induce electron
movement or electron rearrangement.
• By inducing the movement of electrons within
an object, one side of the object is left with an
excess of positive charge and the other side of
the object is left with an excess of negative
charge. Charge becomes separated into
opposites.
• Polarization is not charging – the total charge
in a polarized object is still zero just like before.
The Electroscope
• An electroscope is a device which is capable of detecting
the presence of a charged object through polarization.
Polarization of an electroscope
How Can an Insulator be Polarized?
• In an insulator, electrons merely redistribute
themselves within the atom or molecules nearest the
outer surface of the object.
Polarization is Not Charging
• When an object becomes polarized, there
redistribution
is simply a __________________
of the
centers of positive and negative charges
within the object.
• While there is a separation of charge,
there is NOT an imbalance of charge.
When neutral objects become polarized,
neutral
they are still ______________
objects.
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.
Charging by Friction
Charging by Induction
Charging by Conduction
Grounding - the Removal of a Charge
objectives
• Know:
– Definitions of conduction, induction, and grounding.
– Charge is transferred in solids by electron movement only.
• Understand:
- How charge is transferred by friction, conduction, and
induction.
• Be able to:
- Draw and interpret pith ball and electroscope diagrams.
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.
When wool is rubbed against a PVC
pipe, the PVC steals electrons from
the wool because it has higher
electron affinity compared to wool.
The PVC strip ends
up with a negative charge while the
wool
ends up with a positive charge
When wool is rubbed against a
Nylon strip, the wool will steal
electrons from the Nylon because
wool has higher electron affinity
than Nylon. As a result, the Nylon
ends up positively charged and the
wool ends up negative.
How do we know which object will gain
electrons and which will lose electrons?
• electron affinity determines which object will
gain electrons.
• 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
• The frictional charging process (as well as any
charging process) involves a transfer of
electrons between two objects.
• During all charging processes, the net charge of
the system is conserved.
Charging by Induction
• the charging by induction method is to charge
an object without actually touching the
charged object.
• An understanding of charging by induction
requires an understanding of the nature of a
conductor and an understanding of the
polarization process.
• What is a conductor?
• What is polarization?
Charging by induction - Using a Negatively
Charged Object
Two metal
spheres are
mounted on
insulating
stands
The presence of
a – charge
induces e- to
move from
sphere A to B.
the two-sphere
system is
polarized.
Sphere B is
separated from
sphere A using the
insulating stand. The
two spheres have
opposite charges.
The excess
charge
distributes
itself
uniformly
over the
surface of
the
spheres.
Charging by induction - Using a
Positively Charged Object
Two metal
spheres are
mounted on
insulating
stands
The presence of
a + charge
induces e- to
move from
sphere A to B.
The two-sphere
system is
polarized.
The excess
Sphere B is
charge
separated from
distributes
sphere A using the
itself
insulating stand. The
uniformly
two spheres have
over the
opposite charges.
surface of
the
spheres.
Charging a single sphere by
induction
When touched, the
A metal
A – balloon
sphere is induces e- to e- leave the sphere
mounted move from left through the hand
and enter “the
on
side to the
ground.” The
insulating right side. The
person has
stand
sphere is
replaced the
polarized.
second sphere
(Sphere B) and
serves the role of
the ground.
The sphere is
now charged
positively, with
the excess
charge
attracted to the
balloon.
The positive
charge
evenly
distributes
itself over
the sphere.
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 neutral object got charged through
a ground.
• A ground can serve as a supplier or receiver of
electrons.
Examples of ground
Grounding is also a way of
uncharging an object.
The Need for a Conducting Pathway
• Any object can be grounded provided that the charged
atoms of that object have a conducting pathway between
the atoms and the ground.
Electrons will travel along that pathway.
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 is never touched to the
object being charged by induction.
2. The charged object does not transfer
electrons to or receive electrons from the
object being charged. The charged object
serves to polarize the object being charged.
3. 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).
4. 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
Charging by Conduction
• Charging by conduction involves the contact of a
charged object to a neutral object.
A metal sphere
with an excess of
– charge is
brought near to a
neutral
electroscope.
Upon contact, emove from the
sphere to the
electroscope
and spread
about uniformly.
The metal sphere now
has less excess –
charge and the
electroscope now has
a - charge
• When charging by conduction both object have
the same type of charge when separated.
– If A negatively charged object touches a
neutral object the neutral object gains
electrons and becomes negatively charged as
well.
– If a positively charged object touches a
neutral object then the neutral object loses
electrons and when separated it is positively
charged as well.
• To charge by conduction successfully your
charged and neutral object must be
conductors!
Law of Conservation of Charge
• In a closed system, charge is always
conserved. The total amount of charge among
the objects is the same before the charging
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
• 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.
Lesson 3: Electric Force
1.
2.
3.
4.
Charge Interactions Revisited
Coulomb's Law
Inverse Square Law
Newton's Laws and the Electrical
Force
objectives
Know:
– Definition of electrostatic force.
– Electrostatic force equation
– Inverse square relationship between Fe and r
Understand:
– Relationship between electrostatic force, charge, and
separation distance.
Be able to:
– Use the electrostatic force equation to solve for unknown
variables.
– Sketch or recognize a graph of Fe vs. r
– Predict changes to force based on changes to:
One or both charges
Separation distance
Charge Interactions are Forces
• 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.
A charged PVC pipe and a paper
bit interact. The electrical force
on the paper bit from PVC pipe
balances the weight on the
paper bit. The paper remains in
equilibrium.
Electric force is a non-contact force
• 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.
Two like-charged objects
exert equal and opposite
repulsive electrical force on
each other without contact
with each other.
Free body diagrams for objects A
and B shown that there are three
forces on each of the two objects.
Both Felect and Fgrav are non-contact
forces.
Force as a Vector Quantity
• Being a force, the strength of the electrical interaction is
vector quantity which has both magnitude and
a __________________
direction.
• The best way to determine the direction of it is to apply
the fundamental rules of charge interaction
– opposites ____________.
attract
– likes ____________.
repel
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,
– The ______________
on object 2,
charge
– The _________________
between them.
distance
Q1
r
•k is a proportionality constant known as the Coulomb's law
constant. k = 8.99 x 109 N • m2 / C2.
•F: force between two charges, (in Newtons)
Q2
• 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
• 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.
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.
Comparing Electrical and Gravitational
Forces
• Both electrical force and gravitational force are
non-contact forces.
•The two equations have a very similar form.
inverse square
–Both equations show an _________________
relationship between force and separation distance.
–both equations show that the force is proportional to the
product of the quantity that causes the force.
• 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 is
inverse squared
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
Coulomb’s law – force and charge has
direct relationship
• 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
Newton's Laws and the Electrical Force
• 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 goal of the analysis is not to
determine the acceleration of the object. Instead, 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?
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 the balloons 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
Lesson 4: Electric Fields
1.
2.
3.
4.
5.
Action-at-a-Distance
Electric Field Intensity
Electric Field Lines
Electric Fields and Conductors
Lightning
objectives
Know:
– Electric fields: Exist near charges, originate on positives and
end on negatives, never cross
– Electric field intensity equations.
Understand:
– Relationship between field strength, distance, force and
charge
– Behavior of charges between charged plates
Be able to:
– Use the electric field equation to solve for unknown variables.
– Draw and recognize electric field diagrams for:
Point charges
Systems of charges
Parallel plates
Action-at-a-distance force
• There are two categories of forces - contact
forces and action-at-a-distance forces.
• Electrical force and gravitational force were both
action-at-a-distance 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
The Electric Field and Gravitational
Field Concept
• How can an apple reach across
g = Fg / m
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 mass object enters
that space or not, the gravitational
field exists.
• How can a balloon reach across
space and pull a second balloon
towards it or push it away?
• 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 Field strength
• Electric field strength is a vector quantity. it has
both magnitude and direction.
e
• E is The electric field strength.
• q is the test charge – in Coulombs
• Fe is the force on the test charge q – in
Newton
• Electric field strength is the force per
charge ratio. The unit for electric field is
N/C
e
• 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.
• According to Coulomb's law, Felect = kQq/d2, increasing
the quantity of charge on the test charge - say, by a
factor of 2 - would increase the electric force (F) by a
factor of 2 also, so the ratio of Fe/q still stays the same,
• So regardless of what test charge is used, the electric
field strength at any given location around the source
charge Q will be measured to be the same.
Another Electric Field Strength
Formula
By applying Coulomb’s Law equation, we can deduce
that
GM E
g
d2
• The electric field strength is dependent upon the
Q
quantity of charge on the source charge (______)
and
d
the distance of separation (______)
from the source
charge.
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?
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?
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
The Direction of the Electric Field Vector
vector
• Electric field strength is a _______quantity.
• 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.
_______
• electric field vectors are always directed ____________
towards
negatively-charged objects
Electric Field Lines
• Lines are directed away from positively charged source
charges and toward negatively charged source charges.
• The closer lines near the charge indicating stronger field.
Rules for Drawing Electric Field Patterns
1. Surround more charged objects by
more lines.
_____________________.
greatest
• The electric field is ___________________
at
locations closest to the surface of the charge and
least at locations further from the surface of the
charge.
2.
draw the lines of force ___________________
to the
perpendicular
surfaces of objects at the locations where the lines
connect to object's surfaces.
•
The electric force, and thus the electric field, is always
directed perpendicular to the surface of an object.
There are never any component of force parallel to the
surface.
3.
never cross
Electric field lines should _____________________.
•
Every single location in space has its own electric field
strength and direction associated with it; consequently,
the lines representing the field cannot cross each other
at any given location in space.
Electric Field Lines for Configurations
Two Opposite charges
• two same charges
• At what point is E = 0
0
• Two Unequal amount of charges
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 E=F/q, the __________________________
on a
charged particle everywhere inside the plates.
• A charged particle will accelerate toward the plate with the
opposite charge.
• Ex: negative charge accelerates to positive plate, and
positive charge accelerate to negative plate.
++++++++++++++++++++++++++++++++++++++++++++++
┼
─
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
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
charged conductor is zero.
•
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
entirely on the conductor’s outer surface.
3.
the electric field on the surface of the conductor is
directed entirely perpendicular to the surface.
4.
A forth characteristic of conducting objects at
electrostatic equilibrium is that 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
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?
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]
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
Electric Field and the Movement of Charge
Electric Potential
Electric Potential Difference
objectives
Know:
- Definition of electrical potential; electron-volt
- Unit of electrical potential
- Electrical potential equation
Understand:
- How energy is stored in electric fields.
- Relationship between electrical potential, work, and charge.
- Appropriateness of using electron-volts vs. joules.
Be able to:
- Use the electrical potential equation to:
• Solve for unknown variables.
• Find kinetic energy
- Determine methods for maximizing or minimizing electrical
potential.
- Convert from electron-volts to joules.
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
-e
-e field, its movement is affected by the field.
+e
+e
Electric Field, Work, and Potential Energy
• Electric fields are similar to gravitational fields - both involve
action-at-a-distance forces.
• In the case of gravitational fields, when gravity does work upon
an object to move it in the direction of the gravitational field, then
the object loses potential energy. However, when work is done to
move an object against gravity, the object gains potential energy.
• In a similar manner, when a charge is moved by the electric field,
it loses energy. To move a charge in an electric field against its
natural direction of motion would require work. The exertion of
work by an external force would in turn add potential energy to
the object.
Moving the + test charge against
the E field from A to B will
require work and increase the
potential energy of the charge.
This is similar to an object going
uphill.
The + test charge will naturally
move in the direction of the E field
from B to A; work is not required.
The potential energy of the charge
will decrease. This is similar to an
object going downhill.
One can conclude that the high energy location for a positive test
charge is a location nearest the positive source charge; and the low
energy location is furthest away.
Now consider the motion of the same positive test charge within
the electric field created by a negative source charge. The
same principle regarding work and potential energy will be used
to identify the locations of high and low energy.
The + test charge will naturally
move in the direction of the E field
from A to B; work is not required.
The potential energy of the charge
will decrease.
Moving the + test charge
against the E field from B to A
will require work and increase
the potential energy of the
charge.
One can conclude that the low energy location for a positive test
charge is a location nearest the negative source charge; and the high
energy location is furthest away.
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
Electric potential
• The concept of electric potential is related to the
potential energy of a positive test charge at various
locations within an electric field.
B: high energy location
B
+
A
A: low energy location
The Gravitational Analogy Revisited
• Gravitational potential energy was defined as the energy
stored in an object due to its vertical position above the
Earth.
GPE = mgh
The height, h, is a quantity that
could be used to rate various
locations about the surface of the
Earth in terms of how much
potential energy each kilogram of
mass would possess when placed
there.
The height, h, is known as gravitational potential. It 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.
• The concept of electric potential must have a
similar meaning.
• Electric potential is purely location
dependent. Electric potential is the potential
energy per charge.
• Electric potential is a property of the location
within an electric field.
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;
Suppose that the electric potential at a
given location is 12 Joules per coulomb,
a 2 coulomb object would possess 24
Joules of potential energy at that
location and a 0.5 coulomb object would
experience 6 Joules of potential energy
at the 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
------------------------------------------------------
Check Your Understanding
•
a.
b.
c.
d.
The quantity electric potential is defined
as the amount of _____.
electric potential energy
force acting upon a charge
potential energy per charge
force per charge
• The following diagrams show an electric field (represented
by arrows) and two points - labeled A and B - located within
the electric field. A positive test charge is shown at point A.
For each diagram, indicate
• a) whether work must be done upon the charge to move it
from point A to point B.
• b) indicate the point (A or B) with the greatest electric
potential energy and the greatest electric potential.
1
2
3
4
Electric Potential Difference
• Electric potential is a location-dependent
quantity that expresses the amount of potential
energy per unit of charge at a specified location.
– When a given amount of charge possesses a
relatively large quantity of potential energy at a given
location, then that location is said to be a location of
high electric potential.
– And similarly, if the same charge possesses a
relatively small quantity of potential energy at a given
location, then that location is said to be a location of
low electric potential.
• As we begin to apply our concepts of potential
energy and electric potential to circuits, we will
begin to refer to the difference in electric
potential between two points.
• Consider the task of moving a positive test charge within a
uniform electric field from location A to location B as shown in
the diagram.
In moving the charge against the electric
field from location A to location B, work will
have to be done on the charge by an
external force. The amount of work that is
done is equal to the increase in the
potential energy.
As a result of this change in potential energy, there is also a
difference in electric potential between locations A and B. This
difference in electric potential is represented by the symbol ∆V.
By definition, the electric potential difference is the difference
in electric potential (V) between the final and the initial location
when work is done upon a charge to change its potential energy.
In equation form, the electric potential difference is
• The standard metric unit on electric potential difference is
the volt, abbreviated V and named in honor of Alessandro
Volta.
• 1 Volt = 1 Joule / Coulomb.
If the electric potential difference between
two locations is 1 volt, then one Coulomb
of charge will gain/lose 1 joule of potential
energy when moved between those two
locations. If the electric potential difference
between two locations is 3 volts, then one
coulomb of charge will gain/lose 3 joules Alessandro Giuseppe
of potential energy when moved between Antonio Anastasio Volta
those two locations.
(2/18/1745 – 3/5/1827)
Because electric potential difference is
Italian physicist known for
expressed in units of volts, it is sometimes the development of the first
referred to as the voltage.
electric cell in 1800.
Electron volt (eV)
•
•
•
•
•
If an elementary charge is moved against an
electric field through a potential difference of one
volt, the work done on the charge is:
W = Vq = (1 volt)(1 e) = 1 eV
1 eV aka electron volt is a quantity of energy
needed to move 1 electron (elementary charge)
through a 1 volt of potential difference of one
volt.
W = Vq = (1 volt)(1.6 x 10-19 C) = 1.6 x 10-19 J
1 eV = 1.6 x 10-19 J
Check Your Understanding
• Moving an electron within an electric field
would change the ____ the electron.
a. mass of
b. amount of charge on
c. potential energy of
example
• Moving a point charge of 3.2 ×10-19 C between
points A and B in an electric field requires 4.8
×10-19 J of energy. What is the potential
difference between these two points?
example
• How many eV is required to move 3.2 x 10-19 C
of charge through a potential difference of 5.0
volts?
example
• A helium ion with +2 elementary charges is
accelerated by a potential difference of 5.0x103
volts. What is the kinetic energy acquired in eV
by the ion?
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?
example
• How much energy in eV is needed to
move one electron through a potential
difference of 1.0x102 volts?
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?