5/9/2014
33.1 Electric Fields
Chapter 33
Electric Fields and Potential
33.2 Electric Field Lines
• A useful way to describe an electric field in
place of vectors is with electric field lines,
also called lines of force.
• Where the lines are farther apart, the field is
weaker.
Vector Nature of Forces
• Two point charges are
separated by a distance r
• The unlike charges produce
a attractive force between
them
• The force on q1 is equal in
magnitude and opposite in
direction to the force on q2
• The space around every electric charged is
filled with an electric field.
• An electric field has both magnitude and
direction.
• The magnitude describes the electric
field’s strength.
• The direction of an electric field is always
from positive to negative.
Vector Nature of Electric Forces
• Two point charges are
separated by a distance
r
• The like charges
produce a repulsive
force between them
• The force on q1 is equal
in magnitude and
opposite in direction to
the force on q2
Electrical Forces are Field Forces
• This is the second example of a field force
Recall that Gravity was the first ex.
• Remember, with a field force, the force is
exerted by one object on another object even
though there is no physical contact between
them.
• There are some important differences
between electrical and gravitational forces.
1
5/9/2014
Electrical Force Compared to
Gravitational Force
• Both are inverse square laws.
• The mathematical form of both laws is the
same.
• Electrical forces can be either attractive or
repulsive.
• Gravitational forces are always attractive.
QUICK QUIZ 32.2 ANSWER
(b). By Newton’s third law, the two
objects will exert forces having equal
magnitudes but opposite directions on
each other.
Superposition Principle Example
• The force exerted by
q1 on q3 is F13
• The force exerted by
q2 on q3 is F23
• The total force exerted
on q3 is the vector
sum of F13 and F23
QUICK QUIZ 32.2
Object A has a charge of +2 µC, and
object B has a charge of +6 µC.
Which statement is true:
(a) FAB = –3FBA, (b) FAB = –FBA, or
(c) 3FAB = –FBA
The Superposition Principle
• The resultant force on any one charge equals
the vector sum of the forces exerted by the
other individual charges that are present.
– Remember to add the forces vectorially
Electrical Field
• Maxwell developed an approach to discussing
fields
• An electric field is said to exist in the region of
space around a charged object
– When another charged object enters this electric
field, the field exerts a force on the second
charged object
2
5/9/2014
Electric Field
Electric Field, cont.
• A charged particle, with
charge Q, produces an
electric field in the
region of space around
it
• A small test charge, qo,
placed in the field, will
experience a force
Direction of Electric Field
• The electric field
produced by a
negative charge is
directed toward the
charge
– A positive test charge
would be attracted to
the negative source
charge
QUICK QUIZ 32.4
A Styrofoam ball covered with a conducting
paint has a mass of 5.0 10-3 kg and has a
charge of 4.0 C. What electric field
directed upward will produce an electric
force on the ball that will balance the weight
of the ball?
2
(a) 8.2 10 N/C (b) 1.2 104 N/C (c)
2.0 10-2 N/C (d) 5.1 106 N/C
•
•
•
•
Mathematically, E = F/qo
Use this for the magnitude of the field
The electric field is a vector quantity
The direction of the field is defined to be the
direction of the electric force that would be
exerted on a small positive test charge placed
at that point
Direction of Electric Field, cont
• The electric field
produced by a positive
charge is directed
away from the charge
– A positive test charge
would be repelled
from the positive
source charge
QUICK QUIZ 32.4 ANSWER
(b). The magnitude of the upward
electrical force must equal the weight of
the ball. That is: qE = mg, so
4.0 10-6 C (E) = 5.0 10-3 kg (9.8 m/ss)
E = 5.0 10-3 kg (9.8 m/ss)/4.0 10-6 C
= 1.2 x 104 N/C
3
5/9/2014
QUICK QUIZ 32.5
QUICK QUIZ 32.5 ANSWER
(a). If a test charge is at the center of
the ring, the force exerted on the
test charge by charge on any small
segment of the ring will be balanced
by the force exerted by charge on
the diametrically opposite segment
of the ring. The net force on the test
charge, and hence the electric field
at this location, must then be zero.
A circular ring of radius b has a total
charge q uniformly distributed around
it. The magnitude of the electric field
at the center of the ring is
(a) 0
(b) keq/b2 (c) keq2/b2
(d) keq2/b
(e) none of these.
Electric Field Line Patterns
• Point charge
• The lines radiate equally
in all directions
• For a positive source
charge, the lines will
radiate outward
Electric Field Line Patterns
• For a negative source
charge, the lines will
point inward
Electric Field Line Patterns
• An electric dipole
consists of two equal
and opposite charges
• The high density of lines
between the charges
indicates the strong
electric field in this
region
Electric Field Line Patterns
•
•
•
•
Two equal but like point charges
At a great distance from the
charges, the field would be
approximately that of a single
charge of 2q
The bulging out of the field lines
between the charges indicates
the repulsion between the
charges
The low field lines between the
charges indicates a weak field in
this region
4
5/9/2014
Electric Field Patterns
• Unequal and unlike
charges
• Note that two lines
leave the +2q charge for
each line that
terminates on -q
QUICK QUIZ 32.7
Rank the magnitudes of the electric field at points A, B,
and C in the figure below, largest magnitude first.
Rules for Drawing Electric Field Lines
• The lines for a group of charges must begin on
positive charges and end on negative charges
– In the case of an excess of charge, some lines will begin or
end infinitely far away
• The number of lines drawn leaving a positive charge
or ending on a negative charge is proportional to the
magnitude of the charge
• No two field lines can cross each other
QUICK QUIZ 32.7 ANSWER
A, B, and C. The field is greatest at point
A because this is where the field lines
are closest together. The absence of
lines at point C indicates that the electric
field there is zero.
5
5/9/2014
Conductors in Electrostatic Equilibrium
• When no net motion of charge occurs within a conductor, the
conductor is said to be in electrostatic equilibrium
• An isolated conductor has the following properties:
– The electric field is zero everywhere inside the conducting material
– Any excess charge on an isolated conductor resides entirely on its
surface
– The electric field just outside a charged conductor is perpendicular to
the conductor’s surface
– On an irregularly shaped conductor, the charge accumulates at
locations where the radius of curvature of the surface is smallest (that
is, at sharp points)
Property 1
• The electric field is zero everywhere inside the
conducting material
– Consider if this were not true
• if there were an electric field inside the conductor, the
free charge there would move and there would be a
flow of charge
• If there were a movement of charge, the conductor
would not be in equilibrium
33.3 Electric Shielding
• What happens when a car is struck by lightning?
• An example of electric shielding is a car being
struck by lightning.
• When a car is struck by lightning, the occupants
in the car are safe. This is because the electrons
that strike the car are mutually repelled and
spread over the metal surface, then discharge
into the ground.
• The electric field inside the car is practically
zero.
• Can we shield from Gravity?
• http://www.youtube.com/watch?v=Zi4kXgDBFhw
6
5/9/2014
Property 2
• Any excess charge on an isolated conductor
resides entirely on its surface
– A direct result of the 1/r2 repulsion between like
charges in Coulomb’s Law
– If some excess of charge could be placed inside
the conductor, the repulsive forces would push
them as far apart as possible, causing them to
migrate to the surface
Property 3
• The electric field just
outside a charged
conductor is perpendicular
to the conductor’s surface
– Consider what would happen
it this was not true
– The component along the
surface would cause the
charge to move
– It would not be in equilibrium
Property 4
• On an irregularly
shaped conductor, the
charge accumulates at
locations where the
radius of curvature of
the surface is smallest
(that is, at sharp points)
More on Property 4
•
•
•
•
Any excess charge moves to its surface
The charges move apart until an equilibrium is achieved
The amount of charge per unit area is greater at the flat end
The forces from the charges at the sharp end produce a larger resultant
force away from the surface
Why a lightning rod works
•
More on Electric Flux
Electric Flux
• Field lines penetrating
an area A
perpendicular to the
field
• The product of EA is
the flux,
• In general:
E
E
= E A cos
– The perpendicular to the area A is at an angle to
the field.
– When the area is constructed such that a closed
surface is formed, use the convention that flux
lines passing into the interior of the volume are
negative and those passing out of the interior of
the volume are positive.
= E A cos
7
5/9/2014
33.4 Electrical Potential Energy
• A charged object has potential energy by virtue
of it location in an electric field. This is called
electric potential energy.
• The small positive charge has more potential
energy when it is closer to the positively
charged sphere because work is required to
move it closer.
33.5 Electric Potential
• Electrical potential is the amount of electrical
potential energy per charge.
• The equation for electric potential:
electric potential = electrical
potential energy
____________________________
charge
Work and Potential Energy
• There is a uniform
field between the two
plates
• As the charge moves
from A to B, work is
done in it
• W = F d= q E d
• ΔPE = - W = - q E d
– only for a uniform field
Gravitational
Potential Energy
Electrical
Potential Energy
Depends on location
-- distance from
source of gravity
(ground)
Get more PE by doing
work
Depends on location
-- distance from
source of electric field
Get more PE by doing
work
• The SI unit for electric potential is volt.
• Electric potential is commonly called
voltage.
• Typical voltage sources include:
dry cell (battery)
generator
car battery
Work and Potential Energy
• There is a uniform
field between the two
plates
• As the charge moves
from A to B, work is
done in it
• W = F d= q E d
• ∆PE = -WAB = - qEd
Note: This is only for a
uniform field
8
5/9/2014
Energy and Charge Movements
• A positive charge gains electrical potential energy
when it is moved in a direction opposite the electric
field
• If a charge is released in the electric field, it
experiences a force and accelerates, gaining kinetic
energy
– As it gains kinetic energy, it loses an equal amount of
electrical potential energy
• A negative charge loses electrical potential energy
when it moves in the direction opposite the electric
field
Summary of Positive Charge
Movements and Energy
• When a positive charge is placed in an electric
field
– It moves in the direction of the field
– It moves from a point of higher potential to a
point of lower potential
– Its electrical potential energy decreases
– Its kinetic energy increases
Application – Electrostatic Precipitator
• It is used to remove
particulate matter from
combustion gases
• Reduces air pollution
• Can eliminate
approximately 90% by
mass of the ash and dust
from smoke
Energy and Charge Movements, cont
• When the electric field is
directed downward, point B
is at a lower potential than
point A
• A positive test charge that
moves from A to B loses
electric potential energy
• It will gain the same amount
of kinetic energy as it loses
potential energy
Summary of Negative Charge
Movements and Energy
• When a negative charge is placed in an
electric field
– It moves opposite to the direction of the field
– It moves from a point of lower potential to a point
of higher potential
– Its electrical potential energy decreases
– Its kinetic energy increases
Application – Electrostatic Air Cleaner
• Used in homes to relieve the discomfort of
allergy sufferers
• It uses many of the same principles as the
electrostatic precipitator
9
5/9/2014
Application – Xerographic Copiers
The Xerographic Process
• The process of xerography is used for making
photocopies
• Uses photoconductive materials
– A photoconductive material is a poor conductor of
electricity in the dark but becomes a good electric
conductor when exposed to light
Application – Laser Printer
• The steps for producing a document on a laser
printer is similar to the steps in the xerographic
process
– Steps a, c, and d are the same
– The major difference is the way the image forms of the
selenium-coated drum
• A rotating mirror inside the printer causes the beam of the laser to
sweep across the selenium-coated drum
• The electrical signals form the desired letter in positive charges on
the selenium-coated drum
• Toner is applied and the process continues as in the xerographic
process
• pictures of capacitors
VI. Electrical Energy Storage
• A. Capacitor
– A device used to store energy in a circuit
• B. Simplest capacitor is a pair of conducting
plates separated by a small distance
– Connect to a charging device (like a battery)
– Charge transferred from one plate to other
10
5/9/2014
Capacitance
• C. Discharged when a conducting path is
provided between them
• D. Energy stored in a capacitor = the energy
stored in an electric field
Capacitance, cont
• C = Q/∆V
• Units: Farad (F)
– 1F=1C/V
– A Farad is very large!
• You often will see µF or pF
Applications of Capacitors – Camera
Flash
• The flash attachment on a camera uses a
capacitor
– A battery is used to charge the capacitor
– The energy stored in the capacitor is released
when the button is pushed to take a picture
– The charge is delivered very quickly, illuminating
the subject when more light is needed
• A capacitor is a device used in a variety of
electric circuits
• The capacitance, C, of a capacitor is defined as
the ratio of the magnitude of the charge on
either conductor (plate) to the magnitude of
the potential difference between the
conductors (plates)
Parallel-Plate Capacitor
• The capacitance of a device depends on the
geometric arrangement of the conductors
• For a parallel-plate capacitor whose plates are
separated by air:
C = EoA/d
Where d is the distance between plates, A is the area,
and Eo is the permattivity of free space.
Applications of Capacitors -Computers
• Computers use capacitors
in many ways
– Some keyboards use
capacitors at the bases of
the keys
– When the key is pressed,
the capacitor spacing
decreases and the
capacitance increases
– The key is recognized by
the change in capacitance
11
5/9/2014
Applications
• Defibrillators
– When fibrillation occurs, the heart produces a
rapid, irregular pattern of beats
– A fast discharge of electrical energy through the
heart can return the organ to its normal beat
pattern
33.6 Electric Energy Storage
• A capacitor is a device that can store
electrical energy.
• The energy stored in a capacitor is energy
stored in electric fields.
• In general, capacitors act as energy reservoirs
that can slowly charged and then discharged
quickly to provide large amounts of energy in
a short pulse
This is an
early
VandeGraaff
generator
Demonstrated
by Robert J.
Van de Graaff
History
• Dr. Robert J. Van de Graaff
designed and built the
generator in the early 1900’s.
He was a professor at MIT. This
generator was originally used
as a research tool in early
atom-smashing and high
energy X-ray experiments.
Safety First!
• VandeGraaff: high voltage
(10,000V), low current (electron
flow)
• Wall: low voltage (120V), high
current (lots electrons)
• Heart devices – caution!
33.7 The Van de Graff Generator
• A motor driven rubber belt is supplied electrons. The
electrons are deposited on the metal dome.
• Due to mutual repulsion, the electrons move to the
outside of the metal dome, leaving room for more
electrons to build up.
12
5/9/2014
Quick Quiz
• What is the magnitude of the
force acting on an alpha
particle that is placed in an
electric field of 400 N/C?
Demos
• Streamers
• Krispy treats! Or Smacks?!
• Bubbles
• Space alien crafts
• Fluorescent current - Freaky!
• Hair raising experience!
13