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CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
College Physics B - PHY2054C
Final Review
12/03/2014
My Office Hours:
Tuesday 10:00 AM - Noon
206 Keen Building
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
PHY2054C
1 Final Exam: Wednesday, 10:00 AM - Noon, UPL 101
➜ Take conceptual questions seriously!
2 Some scores are available on Blackboard!
• Check your scores this week and talk to me and/or your
recitation instructor/lab TA in case you have questions.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Outline
1 Coulomb’s Law
Electric Field
Electric Potential
2 Ohm’s Law
Electric Power
Resistors in Series
3 Magnetic Fields
Right-Hand Rule
4 Magnetic Induction
5 EM Waves
6 Optics
Snell’s Law
Lenses
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 1
Two uniformly charged spheres are firmly fastened toand electrically insulated from frictionless pucks on anair table. The charge on sphere 2 is three times thecharge on sphere 1. Which force diagram correctlyshows the magnitude and direction of the electrostaticforces?
A
B
C
D
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Coulomb’s Law
Two uniformly charged spheres are firmly fastened toand electrically insulated from frictionless pucks on anair table. The charge on sphere 2 is three times thecharge on sphere 1. Which force diagram correctlyshows the magnitude and direction of the electrostaticforces?
A
B
C
D
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Coulomb’s Law
Charles-Augustin de Coulomb
(14 June 1736 - 23 August 1806)
F = kq1 q2
r2
k =1
4πǫ0
= 8.99× 109 N ·m2/C2
ǫ0 is called permittivity of free space
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Superposition of Forces
When there are more than two charges in a problem, the
“Superposition Principle” must be used.
1 Find the forces on the charge of interest due to all the
other forces.
2 Add the forces as vectors. ~F = ~F1 +~F2
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Electric Field
The Electric Field is defined as the force exerted on a tiny
positive test charge at that point divided by the magnitude
of the test charge:
• Consider a point in space where
the electric field is ~E .
• If a charge q is placed at the point,
the force is given by ~F = q ~E .
• Unit of the electric field is N/C:
F = kQ q
r 2= q E
E = kQ
r 2
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Electric Potential Energy
The change in electric potential energy is
∆PE elec = −W = −F ∆x = −q E ∆x
The change in potential energy depends only on the endpoints
of the motion.
A positive amount of energy can be stored in a system that is
composed of the charge and the electric field.
Stored energy can be taken out of the system:
• This energy may show up as an increase in the kinetic
energy of the particle.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Two Point Charges
From Coulomb’s Law:
F =k q1q2
r2
The electric potential energy is given by:
PE elec =k q1q2
r=
q1q2
4πǫ0 r
Note that PE elec varies as 1/r while the
force varies as 1/r2.
• PE elec approaches zero when the
two charges are very far apart.
• The electric force also approaches
zero in this limit.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Electric Potential: Voltage
Electric potential energy is a property of a system of charges
or of a charge in an electric field, it is not a property of a single
charge alone.
Electric potential energy can be treated in terms of a test
charge, similar to the treatment of the electric field produced
by a charge:
V =PE elec
q
• Units are the Volt or [V]: 1 V = 1 J/C.
(Named in honor of Alessandro Volta)
• The unit of the electric field can also be given in terms of
the Volt: 1 N/m = 1 V/m.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Outline
1 Coulomb’s Law
Electric Field
Electric Potential
2 Ohm’s Law
Electric Power
Resistors in Series
3 Magnetic Fields
Right-Hand Rule
4 Magnetic Induction
5 EM Waves
6 Optics
Snell’s Law
Lenses
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 2
In the United States and Canada, the standard line voltage
is VRMS = 110 V. In much of the world (Europe, Australia,
Asia), the standard line voltage is VRMS = 220 V.
The light output of a 60 Watt Tallahassee light bulb if used in
Europe would
A be twice as bright.
B be four times as bright.
C be half as bright.
D be one fourth as bright.
E remain the same brightness.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Ohm’s Law
In the United States and Canada, the standard line voltage
is VRMS = 110 V. In much of the world (Europe, Australia,
Asia), the standard line voltage is VRMS = 220 V.
The light output of a 60 Watt Tallahassee light bulb if used in
Europe would
A be twice as bright.
B be four times as bright. P = V I = V 2 /R
C be half as bright. ➜ It must get brighter.
D be one fourth as bright.
E remain the same brightness.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Ohm’s Law
In the United States and Canada, the standard line voltage
is VRMS = 110 V. In much of the world (Europe, Australia,
Asia), the standard line voltage is VRMS = 220 V.
The light output of a 60 Watt Tallahassee light bulb if used in
Europe would
B be four times as bright. P = V I = V 2 /R
How much brighter?
P Europe
V 2Europe
=1
R=
P USA
V 2USA
→ P Europa = P USA ·V 2
Europe
V 2USA
P Europa = 4 P USA
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Electric Power
Reminder:
Ohm’s Law: R = V / I
Energy in a Resistor
• The test charge gained energy when it passed through the
battery.
• It lost energy as it passed through the resistor.
• Energy is converted into heat energy inside the resistor:
• The energy is dissipated as heat.
• It shows up as a temperature increase of the resistor and its
surroundings.
P (Power) =energy transformed
time=
Q V
t= I V
P = I V = I 2 R = V 2 /R
Electric Power
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 3
Two light bulbs, A and B, are connected in series toa constant voltage source. When a wire is connectedacross B as shown, bulb A
A burns more brightly.
B burns as brightly.
C burns more dimly.
D goes out.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Resistors in Series
Two light bulbs, A and B, are connected in series toa constant voltage source. When a wire is connectedacross B as shown, bulb A
A burns more brightly.
B burns as brightly.
C burns more dimly.
D goes out.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Resistors in Series
When current passes through one resistor and then another,
the resistors are said to be in series:
E − I R 1 − I R 2 = 0 Kirchhoff ′s Loop Rule
Any number of resistors can be connected in series. The
resistors will be equivalent to a single resistor with:
R equiv = R 1 + R 2 + R 3 + ...
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Outline
1 Coulomb’s Law
Electric Field
Electric Potential
2 Ohm’s Law
Electric Power
Resistors in Series
3 Magnetic Fields
Right-Hand Rule
4 Magnetic Induction
5 EM Waves
6 Optics
Snell’s Law
Lenses
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 4
A current in a long, straight wire produces a magnetic field.
The magnetic field lines
A go out from the wire to infinity.
B come in from infinity to the wire.
C form circles that pass through the wire.
D form circles that go around the wire.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Right-Hand Rule
A current in a long, straight wire produces a magnetic field.
The magnetic field lines
A go out from the wire to infinity.
B come in from infinity to the wire.
C form circles that pass through the wire.
D form circles that go around the wire.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Right-Hand Rule
Point the thumb of your right hand
in the direction of the current:
• Your thumb will be parallel to
the wire.
• Curling the fingers of your right
hand around the wire gives the
direction of the magnetic field.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 5
Two current-carrying wires are parallel as shown below; the
current is the same in both wires. The current in both wires is
flowing to the right. At a point midway between the wires, the
direction of the net magnetic field is
A to the right→
B to the left←
C into the screen
D out of the screen
E The field is zero. • P
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Right-Hand Rule
Two current-carrying wires are parallel as shown below; the
current is the same in both wires. The current in both wires is
flowing to the right. At a point midway between the wires, the
direction of the net magnetic field is
A to the right→
B to the left←
C into the screen
D out of the screen
E The field is zero.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 6
Two current-carrying wires are parallel as shown below; the
currents are now in the opposite directions. At a point midway
between the wires (point A), the direction of the net magnetic
field is
A to the right→
B to the left←
C into the screen
D out of the screen
E The field is zero.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Right-Hand Rule
Two current-carrying wires are parallel as shown below; the
currents are now in the opposite directions. At a point midway
between the wires (point A), the direction of the net magnetic
field is
A to the right→
B to the left←
C into the screen
D out of the screen
E The field is zero.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 7
The current-carrying wire as shown below is bent into a loop.
At any point in the wire loop, the direction of the net magnetic
field is:
A to the right→
B to the left←
C into the screen
D out of the screen
E The field is zero.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Right-Hand Rule
The current-carrying wire as shown below is bent into a loop.
At any point in the wire loop, the direction of the net magnetic
field is:
A to the right→
B to the left←
C into the screen
D out of the screen
E The field is zero.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Current Loop
Treat the loop as many small pieces
of wire:
• Apply the right-hand rule to
find the field from each piece
of wire.
• Applying superposition gives
the overall pattern shown on
the right.
At the center of the loop:
B =µ0 I
2R
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Outline
1 Coulomb’s Law
Electric Field
Electric Potential
2 Ohm’s Law
Electric Power
Resistors in Series
3 Magnetic Fields
Right-Hand Rule
4 Magnetic Induction
5 EM Waves
6 Optics
Snell’s Law
Lenses
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 8
A double loop of wire (making 2 turns) is in the x-y plane
centered at the origin. A uniform magnetic field is increasing
at constant rate in the negative z direction. In which direction
is the induced magnetic field in the loop?
A In the positive z direction.
B In the negative z direction.
C There is no induced field because of the double loop.
D There is no induced field because the rate of change of
the magnetic field is constant.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Example
A Assume a metal loop in which the magnetic field passes
upward through it.
B Assume the magnetic flux increases with time.
C The magnetic field produced by the induced emf must
oppose the change in flux.
➜ The induced magnetic field must be downward and the
induced current will be clockwise (right-hand rule).
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Another Example
A Assume a metal loop in which the magnetic field passes
upward through it.
B Assume the magnetic flux decreases with time.
C The magnetic field produced by the induced emf must
oppose the change in flux.
➜ The induced magnetic field must be downward and the
induced current will be counterclockwise (right-hand rule).
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Magnetic Induction
A double loop of wire (making 2 turns) is in the x-y plane
centered at the origin. A uniform magnetic field is increasing
at constant rate in the negative z direction. In which direction
is the induced magnetic field in the loop?
A In the positive z direction.
B In the negative z direction.
C There is no induced field because of the double loop.
D There is no induced field because the rate of change of
the magnetic field is constant.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Outline
1 Coulomb’s Law
Electric Field
Electric Potential
2 Ohm’s Law
Electric Power
Resistors in Series
3 Magnetic Fields
Right-Hand Rule
4 Magnetic Induction
5 EM Waves
6 Optics
Snell’s Law
Lenses
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 9
If an electric field wave oscillates north and south (horizontally),
and the electromagnetic wave is traveling vertically straight up,
then what direction does the magnetic field wave oscillate?
A It does not oscillate: the situation is impossible.
B East and west (horizontally)
C North and south (horizontally)
D Up and down (vertically)
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Electromagnetic Waves
If an electric field wave oscillates north and south (horizontally),
and the electromagnetic wave is traveling vertically straight up,
then what direction does the magnetic field wave oscillate?
A It does not oscillate: the situation is impossible.
B East and west (horizontally)
C North and south (horizontally)
D Up and down (vertically)
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Outline
1 Coulomb’s Law
Electric Field
Electric Potential
2 Ohm’s Law
Electric Power
Resistors in Series
3 Magnetic Fields
Right-Hand Rule
4 Magnetic Induction
5 EM Waves
6 Optics
Snell’s Law
Lenses
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 10
A fish swims below the surface of the water at P. An observer
at O sees the fish at
A a greater depth than it really is.
B the same depth.
C a smaller depth
than it really is.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Refraction
A fish swims below the surface of the water at P. An observer
at O sees the fish at
A a greater depth than it really is.
B the same depth.
C a smaller depth than it really is.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Snell’s Law
The ratio c/v is called index of refraction and is denoted by n:
• n = c/v ➜ sin θ 1 = n sin θ 2
A more general statement can be applied to any two materials
with indices of refraction n1 and n2:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 11
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an upright
virtual image?
A F/2
B 2F
C Any value greater than 2F
D This cannot be done with a convex lens.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Image Formation
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an upright
virtual image?
A F/2
B 2F
C Any value greater than 2F
D This cannot be done with a convex lens.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Question 12
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an inverted
virtual image?
A F/2
B 2F
C Any value greater than 2F
D This cannot be done with a convex lens.
CollegePhysics B
Coulomb’sLaw
Electric Field
Electric Potential
Ohm’s Law
Electric Power
Resistors in Series
MagneticFields
Right-Hand Rule
MagneticInduction
EM Waves
Optics
Snell’s Law
Lenses
Image Formation
A convex lens has a focal length of magnitude F . At which of the
following distances from this lens would an object give an inverted
virtual image?
A F/2
B 2F
C Any value greater than 2F
D This cannot be done with a convex lens.
