ELECTROSTATICS
Electrostatics
• electricity at rest.
• Involves electric charges, the
forces between them and how
they behave in materials
SHOCKING STORY
Background
Static
Electricity
There are Four Universal Forces in nature:
1. weak nuclear
2. strong nuclear
3. gravitational - this one we've studied
4. electrical - this one is next
Experiments show us that there are two
kinds of charges. Ben Franklin named
them positive and negative.
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History of
Electrostatics
Atomic Structure
Atoms that have the same number of
protons and electrons = electrically
neutral.
Net charge = zero
Ions have lost or gained electrons =
electrically charged.
Atoms
Proton has the same amount of positive charge
as the electron has negative charge.
 Why don't protons pull oppositely charged
electrons into the nucleus?
 Why don't the protons in a nucleus
mutually repel and fly apart?
[wave nature of e-]
[strong nuclear force]
Conservation of Charge
In the whole universe:
number of + charges = number of charges
• So the universe is electrically neutral!
• Electric charge cannot be created or
destroyed.
Law of Charges
• Likes repel and opposites attract.
Law of Charges
Animated
Electric Charge
• the fundamental quantity that underlies
all electrical phenomena.
• The attraction between positively charged
protons and negatively charged electrons
holds atoms (all matter) together.
• Charged particles have either:
– gained extra electrons ( - charged)
– or lost electrons ( + charged).
• This happens only when electrons move
from one object to another.
• Protons are fixed in the nucleus
Electric Charge
• Charged particles can only lose or
gain whole electrons - so they can
only have whole number multiples of
the charge on an electron.
– Fractions of the charge on an electron
cannot exist alone.
• Electric charge is quantized.
Electric Charge
The unit of charge is the
• COULOMB (C )
• 1 C = the charge (q ) on 6.25 x 1018
electrons
• 1 electron has an elementary charge
= 1.60 x 10-19 C.
• The Coulomb is a fundamental
quantity like grams and meters.
Insulators:
A material whose electrons
seldom move from atom to atom.
• Most insulators are non-metals.
– Electrons are tightly bound to one nucleus and
cannot move around in the material.
Example:
• Electrons can be rubbed onto or off of glass
and rubber but the electrons stay in one
place and cannot move through the
material.
A material whose conduction
electrons are free to move
throughout the material.
• Most metals are conductors.
– In metals the outer shell electrons are
not securely held by one particular
nucleus.
If a conductor carries excess charge,
the excess is distributed over the
surface of the conductor.
Note: Electricity is just a flow of electrons!
http://www.kirkhamelectrics.co.uk/kirkham_images/contact_image.jpg
Conductors
Electroscope
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Device used to detect the presence of
an electrostatic charge.
• Rubber rod rubbed with fur =
negative charge
• Lucite rod rubbed with silk =
positive charge
Electroscope
Grounding
GROUNDING – The earth is a large
reservoir of electrons. You are connected
to the earth.
• When you touch something negative,
excess electrons can flow through you to
the earth.
• When you touch something that is
positive, electrons flow from the earth
through you to the object.
• Grounding makes an object neutral!
Van de Graff Generator
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3 Methods of CHARGING
• Friction
• Conduction
• Induction
Charging by Friction
• removing electrons by rubbing
different materials together.
• When two different insulators are
rubbed together, electrons can be
transferred from one insulator to the
other.
– substance that gains an electron negative (rubber rod)
– substance that loses an electron positive (lucite rod)
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Charging by Conduction
• Conduction is transfer by touching
(contact).
• the flow of electrons through a conductor.
Charging by the flow of electrons.
• The only charges which can move freely
through metals are negative charges
carried by electrons.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Conduction Example
• When a negatively charged • When a positively charged
rod [rubber is negative]
rod [acetate is positive]
touches a neutral
touches a neutral object
conductor excess electrons
excess electrons flow from
flow from a negatively
the object to the positively
charged rod to the
charged rod.
conductor.
neutral
• The object then becomes
negative.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
neutral
• The object then becomes
positively charged.
In conductors, the charge will spread out evenly over the object.
The neutral object (a conductor) will take the same charge as the
charging rod. This transfer is temporary.
Conduction – Electroscope Example
Positive Rod  + Charge
Negative Rod  - Charge
Charging by Induction
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Induction is transfer without touching.
• the charging of an object without direct
contact.
• the process of "rearranging" the charges
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Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Induction – Electroscope Example
Positive Rod
Negative Rod
Temporary Charge  Returns to Neutral after the Charged Rod is Removed
Electroscope Grounding
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Induction
Induction with a Conductor
Induction with an Insulator
Electrical Polarization
occurs when an object’s atoms
rotate in response to an external
charge. This is how a charged
object can attract a neutral one.
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Electrostatics Problem
Two metal spheres, one with a charge of
3C and the other with a charge of -1C
are brought together and then removed.
What is the resulting charge on the first
sphere?
+3C
-1C
Electrostatics Problem
Two metal spheres, one with a charge of 2µC
and the other with a charge of 4µC are
brought together and then removed. The
first sphere is grounded and the second
sphere then comes in contact with a -1µC
sphere What are the resulting charges on
these spheres?
+2µC
+4µC
Electrostatics Problem
Three styrofoam balls are suspended from
insulating threads. Several experiments are
performed on the balls and the following
observations are made:
I. Ball A attracts B and repels C.
II. A negatively charged rod attracts A.
What are the charges, if any, on each ball?
Clicker Understanding
• Two spheres are touching each other. A
charged rod is brought near. The spheres are
then separated, and the rod is taken away. In
the first case, the spheres are aligned with
the rod, in the second case, they are
perpendicular. After the charged rod is
removed, which of the spheres is:
•
i) Positive
•
ii) Negative
•
iii) Neutral
Positive - B
Negative - A
Neutral - C, D
Calculating How Many
Electrons
Since one electron has an elementary
charge (1.6 x 10-19 C), it is possible to
determine how many extra electrons or
how many missing electrons a charged
particle carries:
Q = net charge
Ne 
qe
charge of electron
M = mass of total electrons
Ne 
Me
mass of one electron
.
Atomic Particles
Atomic
Particle
Neutron
Proton
Electron
Charge
(C)
Mass
(kg)
0
1.6 x 10-19
(positive)
-1.6 x 10-19
(negative)
1.67 x 10-27
1.67 x 10-27
9.11 x 10-31
Electrons and Protons have the same magnitude
of charge but opposite signs or direction.
.
Enlightning Question
A lightning bolt transfers about 15 C to
Earth.
• How many electrons are transferred?
• If each water molecule donates one
electron, what mass of water lost an
electron to the lightning? Flm!
• (One mole of water has a mass of 18 g
and 6.022 x 1023 molecules = one mole.)
Coulomb’s Law
The force between charged particles
depends on:
• the charge on each particle
– directly proportional to their
magnitudes
F ~ Q1Q2
• the distance between particles
– inversely proportional to the
square of the distance between
them. F ~ 1/r²
Clicker Understanding
• A small, positive charge is placed
at the black dot. In which case is
the force on the small, positive
charge the largest?
Clicker Understanding
• A small, positive charge is placed
at the black dot. In which case is
the force on the small, positive
charge the smallest?
Coulomb’s Law
The force between charged particles
depends on:
1. the charge on each particle
• directly proportional to their
magnitudes F ~ Q Q
1 2
2. the distance between particles
• inversely proportional to the square
of the distance between them.
kq q
F 1 2
2
r
F ~ 1/r²
Coulomb’s Law
kq q
F 1 2
r2
• F = force in newtons (N)
• k = 9.0 x 109 Nm2/C2 : a constant whose value
depends on the units used and on the medium
(air) between the particles.
• q1 = 1st point charge
unit of Coulomb (C)
nd
• q2 = 2 point charge
• r (distance) in meters (m)
Coulomb’s Law
If q1 and q2 have opposite signs, the force
is attractive with a negative sign.
If q1 and q2 have same signs, the force is
repulsive and has a positive sign.
Clicker Understanding
• All charges in the diagrams below are
of equal magnitude. In each case, a
small, positive charge is placed at the
black dot. In which cases is the force
on this charge to the left?
Clicker Understanding
• All charges in the diagrams below are
of equal magnitude. In each case, a
small, positive charge is placed at the
black dot. In which cases is the force
on this charge zero?
Coulomb’s Law
• The constant of proportionality depends on
the medium.
K = 1/4πε
• The constant ε is called the permittivity
of the medium.
• vacuum - the constant is written εo. The
units of ε are N-1C2m-2, (this is usually
written as Farads per meter, F/m).
• Air K = 1/4πε where K = 9.0 x 109 Nm2/C2
Comparing Gravity and Electricity
J.R. Zacharias, “Science”, March 8, 1957.
• “ …. Coulomb’s law….in all of atomic and
molecular physics, in all solids, liquids, and
gases and in all things that involve our
relationship with our environment, the only
force besides gravity, is some manifestation of
this simple law. Frictional forces, wind forces,
chemical bonds, viscosity, magnetism.…all of
these are nothing but Coulomb’s law….”
Comparing Gravity and Electricity
Newton’s Law of Gravity
Gm1m 2
FG 
r2
Coulomb’s Law
kQ1Q2
FE 
r2
(1) Repulsive or attractive
(1) Always attractive force, G
is a very small number.
force replaces mass with
charge, k is a very large
G = 6.67 x 10-11 Nm2/kg2
number.
(2) Gravitational forces are
9 Nm2/C2
k=
9.0
x
10
very weak, but very
important.
(2) Implies electrostatic
charges are very strong.
(3) Many large bodies have
neutral charge therefore
no net charge – only
gravitational attraction.
Coulomb’s Law Practice
Find the magnitude of the force
between two charges of 1.0 C each
which are 1.0 m apart.
Coulomb’s Law Practice
Two small spheres are 20 cm apart. The
left sphere has a charge of +10.8 µC and
the right sphere has a charge of +12.2
µC
• a. What force acts on each charge?
• b. What is the direction of the force?
+10.8 µC
+ 12.2 µC
Return of the 1’s Rule
• Used when a relative change is asked for
not the actual size of the force
• Example: : How is the force between two
charges affected if the first charge is
doubled, the second charge is tripled, and
the distance between them is halved?
q1 q 2
F k 2
r
F~
(2)(3)
 12 
2
F2=24F1
Multiple Charges
Three point charges lie along the x axis in a
vacuum as shown below. Calculate the
net force acting on q1.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electrostatic Force Vectors
The electrostatic
force is a vector
• magnitude and
direction
When adding
electrostatic forces:
• Take into account
the direction of all
forces
• Use vector
components when
needed
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electric Force Vectors
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Find the magnitude and direction of the net
electrostatic force on q1 for three charges
lying in the xy plane in a vacuum as
shown below.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electric Field
• Michael Faraday developed the concept
of electric fields in the early 1800’s. The
space around every electrically charged
body is filled with an electric field.
When another charge enters the field, an
electric force acts on it.
• Any electric field has both magnitude and
direction.
[What kind of quantity is this?]
Electric Field
• The magnitude of the field at any point is
the force per unit charge.
• To find the magnitude of an electric field:
F
E
q
E= magnitude of electric field
F= force (on q) at that point
q = small, positive test charge
Electric Field
• To normalize the electric field
calculation, eliminating the arbitrary
test charge we can substitute in
Coulomb’s Law for FE
E
FE (1)
q0
FE 
kQ
E 2
r
kQqo (2)
r2
(2)(1)
E
Where Q is the
charge around which
the electric field is
being measured.
1  kQq0 
 2 
q0  r 
Electric Field Strength
Electric Field Strength
F
E

• Electric Field (E ) is sometimes referred to
q
as the electric field strength as it is similar
in concept to gravitational field strength g  F
m
(g )
• Electric force per unit charge
experienced by a small, positive
point charge q
E= magnitude of electric field
kQ
F
E 2
F= force (on q) at that point
E
r
q q = small, positive test charge
E
0
G
0
Electric Field Strength
• Electric Field is a vector quantity so when
calculating the net electric field, it must be
summed per direction
(like forces).  E  E  E  E ...
tot
E
x
 E1x  E2 x  E3 x ...

E
tot

E
2
xtot
 Ey
2
tot
E
y
1
2
3
 E1 y  E2 y  E3 y ...
 E ytot
 Ex
 tot
  tan 1 




Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electric Field Strength Practice
Two positive charges with net charges of
q1= 2C and q2 = 4C respectively are
separated by a distance of three meters.
Calculate where on the line between
them would the electric field equal zero.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electric Field Strength
Clicker Understanding
All charges in the diagram below are of equal
magnitude. In each of the four cases below,
two charges lie along a line, and we consider
the electric field due to these two charges at a
point along this line represented by the black
dot. In which of the cases below is the field to
the right?
Clicker Understanding
All charges in the diagram below are of equal
magnitude. In each of the four cases below,
two charges lie along a line, and we consider
the electric field due to these two charges at a
point along this line represented by the black
dot. In which case is the magnitude of the field
at the black dot the largest?
Clicker Understanding
All charges in the diagram below are of equal
magnitude. In each of the four cases below,
two charges lie along a line, and we consider
the electric field due to these two charges at a
point along this line represented by the black
dot. In which case is the magnitude of the field
at the black dot the smallest?
Electric Field Lines
• Imagine carrying a small positive test
charge around and mapping the direction
of the force on it.
• Lines representing the force vectors are
drawn away from a positive charge
(toward a negative charge). The more
crowded the lines of force, the stronger the
electric field.
Electric Field Lines
• We draw arrows in the direction of the force length is proportional to the strength. Connect
the arrows to get field lines.
• Draw lines of force around a weak, positively
charged sphere.
• Draw lines of force around a strong, negatively
charged sphere.
Single Charge Field
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• Wherever the test charge is
placed, the force will be
directed away from the
charge (or towards the
charge if it is negative).
Therefore, in this case, the
shape of the field is radial.
Field due to two opposite point charges of
equal magnitude
• a vector addition is needed to predict the
direction of the line of force at the point
considered.
• By considering a number of such additions,
we obtain the following shape.
Field due to two opposite point charges of
equal magnitude
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Field due to two opposite point charges
of equal magnitude
Copywrited by Holt, Rinehart, & Winston
Field due to two similar point charges of
equal magnitude
• Using vector addition to predict the direction
of the line of force at various points produces
a shape like this
• At the center of this field is a place where the
magnitude of the electric field strength is
zero. This is called a neutral point.
Field due to two similar point charges
of equal magnitude
Field due to two similar point charges of
equal magnitude
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Electric Field between
Parallel Plates
• In between the plates the field is
uniform (constant magnitude and
direction) except near the ends.
• The curving field at the end is known as an
edge effect and is minimized by making
the plates length much greater than the
separation of the plates.
Clicker Understanding
Two parallel plates have charges of equal
magnitude but opposite sign. What change
could be made to decrease the field strength
between the plates?
A. increase the magnitude of the charge on both plates
B. decrease the magnitude of the charge on both
plates
C. increase the distance between the plates
D. decrease the distance between the plates
E. increase the area of the plates (while keeping the
magnitude of the charges the same)
F. decrease the area of the plates (while keeping the
magnitude of the charges the same)
Electric Fields
• The electric fields around two charges
interact with each other. Draw lines of
force around the following pairs of
charged spheres:
– Two negatively charged spheres
– Two positively charged spheres
– One positive and one negative charged
sphere
Clicker Understanding
• A set of electric field lines is
directed as below. At which of the
noted points is the magnitude of
the field the greatest?
Clicker Understanding
• A set of electric field lines is
directed as below. At which of the
noted points is the magnitude of
the field the smallest?
Clicker Understanding
A dipole is held motionless in a uniform
electric field. For the situation below,
when the dipole is released, which of
the following describes the subsequent
motion?
A. The dipole moves to the right.
B. The dipole moves to the left.
C. The dipole rotates clockwise.
D. The dipole rotates counterclockwise.
E. The dipole remains motionless.
Clicker Understanding
A small sphere is suspended from a string in a
uniform electric field. Several different cases of
sphere mass and sphere charge are presented
in the following table. In which case is the angle
at which the sphere hangs the largest?
Sphere mass (g)
A.
2.0
B.
3.0
C.
2.0
D.
3.0
E.
4.0
Sphere charge (nC)
4.0
4.0
6.0
8.0
9.0
Clicker Understanding
A small sphere is suspended from a string in a
uniform electric field. Several different cases of
sphere mass and sphere charge are presented
in the following table. In which case is the angle
at which the sphere hangs the smallest?
Sphere mass (g)
A.
2.0
B.
3.0
C.
2.0
D.
3.0
E.
4.0
Sphere charge (nC)
4.0
4.0
6.0
8.0
9.0
• In a conductor excess
charge on a conductor
is free to move
• So the charges will
move until they are as
far apart as possible.
• This results in the
excess charge on a
conductor always being
equally distributed on
its surface.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electric Fields of Conductors
Electric Fields of Conductors
• Since the charge is equally
distributed on a conductor’s
surface, the net electric field
in a conductor is zero.
Physics for the IB Diploma 5th Edition (Tsokos) 2008
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Electric Fields of Conductors
• In addition the electric field
lines are always perpendicular
to the surface of a conductor.
• If not, the charge would move.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Electric Fields of Conductors
• Since charge is equally
distributed on the surface of
a conductor.
• Charge is concentrated where
the shape is more sharply
curved.
• Resulting in a larger electric
field at the more sharply
curved areas.
Lightning
Lightning Rod
• How do they work?
Electropotential Energy
• Work is required to push a small
positive charge against the electric field around a
positively charged sphere.
• Since work is done on the little charge, its PE
increases.
• The closer it gets, the more strongly it is repelled by
the field ……. Therefore more work is required.
• If the charge were released, it would move away
from the sphere and its PE would decrease. Its
kinetic energy would increase.
Electropotential Energy
• When the little charge is added to the
sphere, the charge on the sphere
increases and the field around it
becomes stronger.
• Moving another positive charge toward
the sphere will take even more work or
energy and give the little charge higher
Potential Energy.
Electropotential Energy
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
• Analogous to Mechanical Potential Energy
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Voltage
Potential difference (between 2 points)
• The amount of work done per unit charge
to move a point charge from one point to
the other.
Electrical potential (at a point P)
• Amount of work done per unit charge as
a small positive test charge q is moved
from infinity to the point P.
• Because the unit for potential difference is the volt V, potential
difference is often called voltage and uses the symbol V.
Voltage
• The equation for calculating voltage is:
W Ep
V= =
q
q
symbols
V =
voltage
W=
Work
Ep =
Electrical potential energy
q =
small, positive point charge
units
(V)
(J)
(J)
(C)
• Since work done on a charge and the gain in potential
energy of the charge are the same, voltage can also be
thought of as work per unit charge.
What theorem is this based on?
Electrical Potential
• Potential at a distance r from a Point
Charge Q
• It can be shown that the potential at p is given by
or
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Summing Up Electrical Potential
The electric potential of a group of
point charges is the algebraic sum of
the potentials of each charge.
Vtot  V1  V2  V3 ...
Clicker Understanding
• Rank in order, from largest to
smallest, the electric potentials at
the numbered points.
a) 1 = 2,3
b) 3, 1 = 2
c) 3, 2, 1
d) 1 = 2, 3 = 4
e) 1, 2, 3
Electrical Potential Energy
• If the potential at point p is VP and an
additional charge q is placed at P then
EP = qV
q
• Where EP is the electrical potential energy of
charge q.
• We can also define the electrical potential
energy as the work required to move the charge
from infinity to its current position.
Electrical Potential Energy
• When the positive charge q is at some
distance r from Q, it experiences a
repulsive force
F
kQq
r2
q
• So a force to the left would be required to
move q closer to Q and the work dW done
kQq
over a small distance, dr is
dW   Fdr  
dr
r
• Integrating (calculus)
2
R
kQq
kQq
W    2 dr 
r
r

R

kQq

R
kQq
EP =
r
Electrical Potential Energy
Physics for the IB Diploma 5th Edition (Tsokos) 2008
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
• Both electrical potential energy UE and
electrical potential V are scalars.
• So the change in either potential energy or
potential is path independent.
a) 0;
b) negative;
c) positive;
d) negative;
e) zero;
Is the change ∆EP of the particle positive,
f) negative;
negative, or zero as it moves from i to
f?
g) zero
Clicker Understanding
Electron Volt (eV)
• Unit of work (or energy) much smaller
than the Joule.
• If 1 electron moves through a potential
difference of 1V then 1 eV of work is
done.
• W = Vq and 1 eV is the work done
moving one electron through a
potential difference of 1 V.
• Therefore,
1eV = 1.6×10-19J
Electrical Potential Energy
• Another form of Electrical Potential
Energy is shown by
(1)
kQq
EP =
r
æ kQ ö
EP = ç 2 ÷ qr = Eqr
è (2)(1)
r ø
kQ
E  (2)2
r
EP = Eqd
• From this a relationship between
Electric Field (E ) and Electric Potential
(V ) can be derived
• Recall, V = DEq so E = Eqd = DV
Dd
P
P
Voltage & Electric Field
V
E
d
From calculus the
relationship is
• The electric field is related to
how fast the potential is
changing
• If electrical potential is
graphed versus distance, the
electric field is the slope of
the graph.
E
dV
dr
• This relationship implies that
when the potential is constant
then the electric field is zero.
• So in a conductor where the
electric field is zero, the voltage
must be constant.
• All points on the surface of a
charged conductor are at the
same potential.
• A surface with the same
potential is know as an
equipotential.
V
d
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Voltage & Electric Field
E
Potential due to a Charged
Hollow Metal Sphere
• Outside the sphere the charge can be
considered to be a point charge
placed at the center.
• Inside the sphere, there is no electric field
so all points are at the same potential
as the surface.
Potential due to a Charged
Hollow Metal Sphere
• Graphically, this is represented in a plot of
Electric Potential V vs. distance from the
center of a charged sphere r as:
Physics for the IB Diploma 5th Edition (Tsokos) 2008
Physics for the IB Diploma 5th Edition (Tsokos) 2008
What would a graph of Electric Field E vs distance from
the center of a charged sphere look like?
Equipotentials
• An equipotential in a field is a line (or surface)
joining all points which have the same potential.
• An equipotential is therefore a line (or surface)
along which a charge can be moved without
work being done against (or by) the electric
field.
• This means that equipotentials must always be
at 90° to electric field lines so equipotentials
near a single point charge are spherical.
Equipotentials
• Equipotential Lines
• Moving along Equipotential Lines
• Moving between Equipotential Lines
Voltage & Electric Field
V
E
d
• The relationship between voltage and
electric field is shown graphically in electric
field lines and equipotential lines
• Electric field lines are always
perpendicular to equipotential lines.
Equipotential Surfaces and the Electric Field
•An ideal conductor is an equipotential surface.
• Therefore, if two conductors are at the same
potential, the one that is more curved will have a
larger electric field around it. This is also true for
different parts of the same conductor as stated
earlier.
Copyright ©2007 Pearson Prentice Hall, Inc.
Copyright ©2007 Pearson Prentice Hall, Inc.
Electric Field – Parallel Plates
• The field that exists between two charged
parallel plates (like those on a bug zapper) is
uniform EXCEPT near the plate edges, and
depends upon the potential difference
between the plates and the distance
between the plates.
Electric Field = Potential Difference
distance between plates
V
E
d
Problems
If a conductor connected to the terminal of a
battery has a potential difference (voltage) of
12 V, then each Coulomb of charge has a
potential energy of _______J.
If a charge of 2 x 10-5 C has a PE of 540 J, its
voltage is ____________________V.
If a rubber balloon is charged to 5000 V, and the
amount of charge on the balloon is 1 x 10-7 C,
then the potential energy of this charge is
___________J.
Problems
A force of .032 N is required to move a
charge of 4.2 x 10-6 C in an electric field
between two points which are .25 m
apart. What is the potential difference
(voltage) between the points?
Electric Field Problems
•
If an electron loses 1.4 x 10-15J of energy
in traveling from the cathode to the
screen of Andy’s computer screen, across
what potential different must it travel?
• Chippy stands next to the Van De Graaff
generator and gets a shock as she hold
her knuckle 0.2 m from the machine. In
order for a spark to jump, the electric
field strength must be 3 x 106 V/m. At this
distance, what is the potential difference
between Chippy and the generator?
Similarities between Electric Fields
and Gravitational Fields
Physics for the IB Diploma 5th Edition (Tsokos) 2008