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One reason why we know that magnetic fields are not
the same as electric fields is because the force
exerted on a charge +q
A.
B.
C.
D.
E.
is in opposite directions in
electric and magnetic fields.
is in the same direction in electric
and magnetic fields.
is parallel to a magnetic field and
perpendicular to an electric field.
is parallel to an electric field and
perpendicular to a magnetic field.
is zero in both if the charge is not
moving.
56%
25%
7%
6%
6%
A spatially uniform magnetic field cannot exert a
magnetic force on a particle in which of the following
circumstances? There may be more than one correct
statement.
50%
A.
B.
C.
D.
E.
The particle is charged.
The particle moves perpendicular
to the magnetic field.
The particle moves parallel to the
magnetic field.
The magnitude of the magnetic
field changes with time.
The particle is at rest.
33%
14%
1%
2%
A proton moving horizontally enters a region where a uniform
magnetic field is directed perpendicular to the proton’s velocity
as shown in Figure. After the proton enters the field, it
A.
B.
C.
D.
E.
is deflected downward, with its speed
remaining constant.
is deflected upward, moving in a semicircular
path with constant speed, and exits the field
moving to the left.
continues to move in the horizontal direction
with constant velocity.
moves in a circular orbit and become trapped
by the field.
is deflected out of the plane of the paper.
53%
32%
6%
5%
4%
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Electron A is fired horizontally with speed v into a region where
a vertical magnetic field exists. Electron B is fired along the
same path with speed 2v. Which electron has a path that
curves more sharply?
79%
A.
B.
C.
D.
A does.
B does.
The particles follow the
same curved path.
The particles continue to go
straight.
15%
5%
1%
A particle with electric charge is fired into a region of space
where the electric field is zero. It moves in a straight line.
Can you conclude that the magnetic field in that region is
zero?
A.
B.
C.
D.
E.
Yes, you can.
No; the field might be perpendicular
to the particle’s velocity.
No; the field might be parallel to the
particle’s velocity.
No; the particle might need to have
charge of the opposite sign to have
a force exerted on it.
No; an observation of an object
with electric charge gives no
information about a magnetic field.
86%
4%
5%
2%
3%
A charged particle in a vacuum travels in a helix along
x direction. Which is true?
77%
A.
B.
C.
D.
Both uniform electric and magnetic
fields are required.
Only a uniform electric field is required.
Only a uniform magnetic field is
required.
No fields are required.
16%
7%
0%
A charged particle in vacuum travels in a helix along x direction.
What is the minimum requirement to create the motion?
81%
A.
B.
C.
D.
Magnetic field along x direction and
velocity along x direction.
Magnetic field along x direction and
velocity along x and y direction.
Magnetic field along x direction and
velocity along y direction.
Magnetic field along y direction and
velocity along x and y direction.
4%
8%
7%
In the velocity selector shown in
Figure, electrons with speed v=E/B
follow a straight path. Electrons
moving significantly faster than this
speed through the same selector will
move along what kind of path?
67%
A.
B.
C.
D.
a circle
a straight line
a path moving toward the red plate
A path moving toward the blue plate
13%
2%
18%
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A straight wire is bent into the shape shown. Determine
the net magnetic force on the wire.
54%
28%
A.
B.
C.
D.
E.
Zero
IBL in the +z direction
IBL in the –z direction
1.7 IBL in the +z direction
1.4 IBL in the –z direction
6%
6%
6%
A coaxial cable has an inner cylindrical conductor surrounded by
cylindrical insulation and a thick outer cylindrical conducting shell.
The inner and outer conductors carry the same current but in
opposite directions. If the coaxial cable sits in a uniform magnetic
field as in the figure, the effect of the field on the cable is
A.
B.
C.
D.
E.
a net force to the left.
a net force to the right.
a net force upwards.
no net force but a slight shift
of the inner conductor to the
left and the outer conductor to
the right.
no net force but a slight shift
of the inner conductor to the
right and the outer conductor
to the left.
30% 30%
20%
14%
7%
A straight wire is bent into the shape shown. Determine
the net magnetic force on the wire when the current I
travels in the direction shown in the magnetic field B.
79%
A.
B.
C.
D.
E.
2IBL in the –z direction
2IBL in the +z direction
4IBL in the +z direction
4IBL in the –z direction
zero
8%
4%
6%
4%
A straight wire is bent into the shape shown. Determine
the net magnetic force on the wire.
57%
A.
B.
C.
D.
E.
Zero
IBL in the +z direction
IBL in the –z direction
1.7 IBL in the +z direction
1.4 IBL in the –z direction
20%
15%
4%
5%
A coaxial cable has an inner cylindrical conductor surrounded by
cylindrical insulation and a thick outer cylindrical conducting shell.
The inner and outer conductors carry the same current but in
opposite directions. If the coaxial cable sits in a uniform magnetic
field as in the figure, the effect of the field on the cable is
A.
B.
C.
D.
E.
a net force to the left.
a net force to the right.
a net force upwards.
no net force but a slight shift
of the inner conductor to the
left and the outer conductor to
the right.
no net force but a slight shift
of the inner conductor to the
right and the outer conductor
to the left.
59%
5%
3%
20%
14%
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A magnetic field exerts a torque on each of the current carrying
single loops of wire shown in Figure. The loops lie in the xy
plane, each carrying the same magnitude current, and the
uniform magnetic field points in the positive x direction. Rank
the loops by the magnitude of the torque exerted on them by the
field from largest to smallest.
A.
B.
C.
D.
AA > AC > AB
AB > AA > AC
Ac > AB > AA
AA > AB > AC
25%
25%
25%
25%
:45
Consider the magnetic field due to the current in the length of
wire shown in Figure 30.2. Rank the points A, B, and C in terms
of magnitude of the magnetic field that is due to the current in
just the length element ds shown from greatest to least.
25%
A.
B.
C.
D.
25%
25%
25%
B>A>C
A>B>C
B>C>A
C>A>B
:45
Rank the magnitudes of the net forces acting on the rectangular
loops shown in Figure from highest to lowest. All loops are
identical and carry the same current.
25%
A.
B.
C.
D.
25%
25%
25%
(a) = (b) = (c)
(c) > (b) > (a)
(a) = (c) > (b)
(b) > (c) > (a)
:45
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Rank the magnitudes of the net forces acting on the rectangular
loops shown in Figure from highest to lowest. All loops are
identical and carry the same current.
80%
A.
B.
C.
D.
(a) = (b) = (c)
(c) > (b) > (a)
(a) = (c) > (b)
(b) > (c) > (a)
15%
4%
2%
Rank the magnitudes of the torques acting on the rectangular
loops (a), (b), and (c) shown edge-on in Figure from highest to
lowest. All loops are identical and carry the same current.
A.
B.
C.
D.
(a) = (b) = (c)
(c) > (b) > (a)
(a) = (c) > (b)
(b) > (c) > (a)
68%
5%
10%
17%
A magnetic field exerts a torque on each of the current carrying
single loops of wire shown in Figure. The loops lie in the xy
plane, each carrying the same magnitude current, and the
uniform magnetic field points in the positive x direction. Rank
the loops by the magnitude of the torque exerted on them by the
field from largest to smallest.
A.
B.
C.
D.
AA > AC > AB
AB > AA > AC
Ac > AB > AA
AA > AB > AC
79%
6%
5%
10%
In Figure, assume I1 = 2 A and I2 = 6 A. What is the relationship
between the magnitude F1 of the force exerted on wire 1 and
the magnitude F2 of the force exerted on wire 2?
44%
27%
A.
B.
C.
D.
E.
F1 = 6F2
F1 = 3F2
F1 = F2
F1 = F2/3
F1 = F2/6
20%
8%
1%
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Three coplanar parallel straight wires carry equal currents I to
the right as shown below. Each pair of wires is a distance a
apart. The direction of the magnetic force on the middle wire
A.
B.
C.
D.
E.
is up out of the plane of the wires.
is down into the plane of the wires.
is in the plane of the wires, directed
upwards.
is in the plane of the wires, directed
downwards
cannot be defined, because there
is no magnetic force on the middle
wire.
20% 20% 20% 20% 20%
:30
A thin infinitely large current sheet lies in the plane as in Figure
below. Current of magnitude J per unit length travels out of the
page. Which diagram below correctly represents the direction of
the magnetic field on either side of the sheet?
A.
.
B.
.
C.
.
D.
.
E.
.
20% 20% 20% 20% 20%
:30
In Figure, assume I1 = 2 A and I2 = 6 A. What is the relationship
between the magnitude F1 of the force exerted on wire 1 and the
magnitude F2 of the force exerted on wire 2?
20%
A.
F1 = 6F2
B.
F1 = 3F2
C.
F1 = F2
D.
F1 = F2/3
E.
F1 = F2/6
20%
20%
20%
20%
:45
Two long, parallel wires carry currents of 20.0 A and 10.0 A in
opposite directions in the Figure. Which of the following
statements is true? More than one statement may be correct.
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
In region I, the magnetic field is into
the page and is never zero.
In region II, the field is into the
page and can be zero.
In region III, it is possible for the
field to be zero.
In region I, the magnetic field is out
of the page and is never zero.
There are no points where the field
is zero.
:45
Three coplanar parallel straight wires carry equal currents I to
the right as shown below. Each pair of wires is a distance a
apart. The direction of the magnetic force on the middle wire
A.
B.
C.
D.
E.
is up out of the plane of the wires.
is down into the plane of the wires.
is in the plane of the wires, directed
upwards.
is in the plane of the wires, directed
downwards
cannot be defined, because there
is no magnetic force on the middle
wire.
20% 20% 20% 20% 20%
:45
A thin infinitely large current sheet lies in the plane as in Figure
below. Current of magnitude J per unit length travels out of the
page. Which diagram below correctly represents the direction of
the magnetic field on either side of the sheet?
A.
.
B.
.
C.
.
D.
.
E.
.
20%
20%
20%
20%
20%
:45
Consider the two parallel wires carrying currents in opposite
directions in Figure OQ30.9. Due to the magnetic interaction
between the wires, the lower wire experiences a magnetic force
that is:
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
upward.
downward.
to the left.
to the right.
into the paper.
:30
Consider the magnetic field due to the current in the length of
wire shown in Figure 30.2. Rank the points A, B, and C in terms
of magnitude of the magnetic field that is due to the current in
just the length element ds shown from greatest to least.
25%
A.
B.
C.
D.
25%
25%
25%
B>A>C
A>B>C
B>C>A
C>A>B
:45
A loose spiral spring carrying no current is hung from a
ceiling. When a switch is thrown so that a current
exists in the spring, the coils:
20%
20%
20%
20%
20%
A.
B.
C.
D.
move closer together.
move farther apart.
rotate clockwise
rotate counter
clockwise
E. do not move at all.
:45
Chapter 30.4-6
Day 29
Clicker (physical one) :
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What happens to the magnitude of the magnetic field inside a
long solenoid if the radius is doubled?
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
It becomes four times larger.
It becomes twice as large.
It is unchanged.
It becomes one-half as large.
It becomes one-fourth as large.
:30
Ampere’s law: Example, solenoid
Ampere’s law: Examples, infinite plane and Toroid
Magnetic flux! An example
What happens to the magnitude of the magnetic field inside a
long solenoid if the radius is doubled?
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
It becomes four times larger.
It becomes twice as large.
It is unchanged.
It becomes one-half as large.
It becomes one-fourth as large.
:45
Solenoid A has length L and N turns, solenoid B has length 2L
and N turns, and solenoid C has length L/2 and 2N turns. If
each solenoid carries the same current, rank the magnitudes of
the magnetic fields in the centers of the solenoids from largest
to smallest.
33%
A. C > A > B
B. A > B > C
C. B > C > A
33%
33%
:45
An ideal solenoid of radius a has n turns per unit length and
current I. The magnetic flux ΦB through any circular area of
radius a inside the solenoid, centered on and perpendicular to
the solenoid axis is
 a2
0
nI
A. . 2
 a2
B. . 0
nI
C. . 4
20% 20% 20% 20% 20%
D. . 0 a 2 nI
E. 0.
2 0 a 2 nI
:45
Magnetic Moment of Atom
- constant speed v
- a circular orbit of radius r
- travels a distance 2r in a time interval T
Bohr magneton
 B = 9.27 x 10-24 J/T
- Ferromagnetism
- Paramagnetism
- Diamagnetism
What is the magnitude and direction of the magnetic
field at point P in unit of (I times mu0)?
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
(b-a)/(8ab) into the page
(b-a)/(8ab) out of the page
(b-a)/(2ab) into the page
(b-a)/(2ab) out of the page
0.
:45
Two long, parallel wires carry currents of 20.0 A and 10.0 A in
opposite directions in the Figure. Which of the following
statements is true? More than one statement may be correct.
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
In region I, the magnetic field is into
the page and is never zero.
In region II, the field is into the
page and can be zero.
In region III, it is possible for the
field to be zero.
In region I, the magnetic field is out
of the page and is never zero.
There are no points where the field
is zero.
:45
In Figure, assume I1 = 2 A and I2 = 6 A. What is the relationship
between the magnitude F1 of the force exerted on wire 1 and the
magnitude F2 of the force exerted on wire 2?
20%
A.
F1 = 6F2
B.
F1 = 3F2
C.
F1 = F2
D.
F1 = F2/3
E.
F1 = F2/6
20%
20%
20%
20%
:45
Consider the magnetic field due to the current in the length of
wire shown in Figure. Rank the points A, B, and C in terms of
magnitude of the magnetic field that is due to the current in just
the length element ds shown from greatest to least.
25%
A.
B.
C.
D.
25%
25%
25%
B>A>C
A>B>C
B>C>A
C>A>B
:45
Consider the two parallel wires carrying currents in opposite
directions in Figure. Due to the magnetic interaction between
the wires, the lower wire experiences a magnetic force that is:
20% 20% 20% 20% 20%
A.
B.
C.
D.
E.
upward.
downward.
to the left.
to the right.
into the paper.
:30
Three coplanar parallel straight wires carry equal currents I to
the right as shown below. Each pair of wires is a distance a
apart. The direction of the magnetic force on the middle wire
A.
B.
C.
D.
E.
is up out of the plane of the wires.
is down into the plane of the wires.
is in the plane of the wires, directed
upwards.
is in the plane of the wires, directed
downwards
cannot be defined, because there
is no magnetic force on the middle
wire.
20% 20% 20% 20% 20%
:45
A thin infinitely large current sheet lies in the plane as in Figure
below. Current of magnitude J per unit length travels out of the
page. Which diagram below correctly represents the direction of
the magnetic field on either side of the sheet?
A.
.
B.
.
C.
.
D.
.
E.
.
20%
20%
20%
20%
20%
:45
A loose spiral spring carrying no current is hung from a
ceiling. When a switch is thrown so that a current
exists in the spring, the coils:
20%
20%
20%
20%
20%
A.
B.
C.
D.
move closer together.
move farther apart.
rotate clockwise
rotate counter
clockwise
E. do not move at all.
:45
Chapter 31.1-2
Day 31
A rectangular conducting loop is placed near a long wire carrying
a current I as shown in Figure. If I decreases in time, what can be
said of the current induced in the loop?
53%
A.
B.
C.
D.
E.
The direction of the current depends
on the size of the loop.
The current is clockwise.
The current is counterclockwise.
The current is zero.
Nothing can be said about the current
in the loop without more information.
30%
11%
4%
1%
The Figure is a graph of the magnetic flux through a certain coil of
wire as a function of time. Rank the emf induced in the coil at the
instants marked A through E from the largest positive value to the
largest-magnitude negative value. In your ranking, note any cases of
equality and also any instants when the emf is zero.
32%
32%
25%
12%
A.
B.
C.
D.
C=D>B=A>E
E>A=B=0>C>D
A>B>D>C>E
E>A>B=D=0>C
Faraday’s law of Induction
d B
ε
dt
B   B  dA
Assume a loop enclosing
an area A lies in a uniform
magnetic field.
The magnetic flux through
the loop is ΦB = BA cos θ.
The induced emf is
ε = - d/dt (BA cos θ).
Magnetic flux! An example with I(t)=p +q t
Example of Faraday’s Law
The Figure is a graph of the magnetic flux through a certain coil of
wire as a function of time. Rank the emf induced in the coil at the
instants marked A through E from the largest positive value to the
largest-magnitude negative value. In your ranking, note any cases of
equality and also any instants when the emf is zero.
58%
41%
A.
B.
C.
D.
C=D>B=A>E
E>A=B=0>C>D
A>B>D>C>E
E>A>B=D=0>C
1%
1%
A bar magnet is held in a vertical orientation above a loop of
wire that lies in the horizontal plane as shown in Figure. The
south end of the magnet is toward the loop. After the magnet is
dropped, what is true of the induced current in the loop as
viewed from above?
A.
B.
C.
D.
E.
It is clockwise as the magnet falls
toward the loop.
It is counterclockwise as the magnet
falls toward the loop.
It is clockwise after the magnet has
moved through the loop and moves
away from it.
It is always clockwise.
It is first counterclockwise as the
magnet approaches the loop and
then clockwise after it has passed
through the loop.
49%
22%
14%
13%
2%
The bar in Figure moves on rails to the right with a velocity v, and
a uniform, constant magnetic field is directed out of the page.
Which of the following statements are correct? More than one
statement may be correct.
36% 34%
A.
B.
C.
D.
E.
The induced current in the loop is zero.
The induced current in the loop is clockwise.
The induced current in the loop is
counterclockwise.
An external force is required to keep the bar
moving at constant speed.
No force is required to keep the bar moving at
constant speed.
16%
10%
5%
Motional EMF
Chapter 31.2-4
Day 32
A square, flat loop of wire is pulled at constant velocity through a
region of uniform magnetic field directed perpendicular to the
plane of the loop as in Figure. Is current induced in the loop?
66%
23%
A.
B.
C.
yes, clockwise
yes, counterclockwise
no
11%
A square, flat loop of wire is pulled at constant velocity through a
region of uniform magnetic field directed perpendicular to the
plane of the loop as in Figure. Does charge separation occur in
the coil?
88%
A.
B.
C.
yes, with the top edge positive
yes, with the top edge negative
no
4%
8%
Motional EMF
Does current induced? Why? Why not?
A metal rod of length L in a region of space where a constant
magnetic field points into the page rotates clockwise about an
axis through its center at constant angular velocity w. While it
rotates, the point(s) at highest potential is(are)
79%
A.
B.
C.
D.
E.
F.
A.
B.
C.
B and D.
A and E.
None of the above
11%
8%
1%
1%
0%
The bar in Figure moves on rails to the right with a velocity v, and
a uniform, constant magnetic field is directed out of the page.
Which of the following statements are correct? More than one
statement may be correct.
48%
A.
B.
C.
D.
E.
The induced current in the loop is zero.
The induced current in the loop is clockwise.
The induced current in the loop is
counterclockwise.
An external force is required to keep the bar
moving at constant speed.
No force is required to keep the bar moving at
constant speed.
1%
47%
2%
1%
A square, flat loop of wire is pulled at constant velocity through
a region of uniform magnetic field directed perpendicular to the
plane of the loop as in Figure. Does charge separation occur in
the coil?
96%
A.
B.
C.
yes, with the top edge
positive
yes, with the top edge
negative
no
1%
3%
Chapter 31.3-6
Day 33
- HW 10 is due on Thursday, 11/10
- Midterm 3 is on 11/21
Two bulbs are shown in a circuit that surrounds a region of
increasing magnetic field directed out of the page. When
the switch is closed,
53%
A.
B.
C.
D.
E.
bulb 1 glows more brightly.
bulb 2 glows more brightly.
both bulbs continue to glow
with the same brightness.
bulb 1 goes out.
bulb 2 goes out.
33%
10%
3%
1%
Starting outside the region with the magnetic field, a coil of wire enters,
moves across, and then leaves (at constant velocity v) a region with a
uniform magnetic field perpendicular to the page. As seen from above, a
counterclockwise emf is regarded as positive. In which direction did the
loop move over the plane of the page?
53%
A.
B.
C.
D.
E.
The loop moved from bottom to top.
The loop moved from top to bottom.
The loop moved from left to right.
The loop moved from right to left.
All of these directions of motion will
produce the graph of emf vs t.
28%
15%
1%
3%
Lenz’s Law : induced current in a loop is in the
direction that creates B that opposes the change!!
Induced EMF and Electric field
AC current generator
Eddy currents
Chapter 32.1-2
Day 34
Exam 3
--- date : November 21, Monday at class.
--- Please remember your official section.
--- Materials covered : Chapter 29, 30, 31 and 32 of the textbook,
lectures, recitation materials, and homework 8-11.
--- Student ID & Black lead pencil (# 2 1/2 or softer)
--- No calculator, no phone, no laptop, no scratch papers are allowed
Eddy currents
Starting outside the region with the magnetic field, a coil of wire
enters, moves across, and then leaves a region with a uniform
magnetic field perpendicular to the page. The loop moves at constant
velocity v. As seen from above, a counterclockwise emf is regarded as
positive. In which direction did the loop move over the plane of the
page?
42%
26%
A.
B.
C.
D.
E.
The loop moved from bottom to top.
The loop moved from top to bottom.
The loop moved from left to right.
The loop moved from right to left.
All of these directions of motion will
produce the graph of emf vs t.
21%
10%
2%
Two coils are placed near each other as in Figure. The coil on the
left is connected to a battery and a switch, and the coil on the right
is connected to a resistor. What is the direction of the current in the
resistor at an instant immediately after the switch is thrown closed?
80%
A.
B.
C.
left
right
the current is zero
17%
3%
Two bulbs are shown in a circuit that surrounds a region of
increasing magnetic field directed out of the page. When
the switch is closed,
89%
A.
B.
C.
D.
E.
bulb 1 glows more brightly.
bulb 2 glows more brightly.
both bulbs continue to glow
with the same brightness.
bulb 1 goes out.
bulb 2 goes out.
3%
2%
6%
1%
Ch. 32
-- we are dealing with a time dependent
phenomena!!
Self Inductance
dI
εL  L
dt
[L] = [Volt sec / A ] = [H]enry
Inductance of Solenoid
A coil with zero resistance has its ends labeled a and b.
The potential at a is higher than at b. Which of the
following could be consistent with this situation?
A.
B.
C.
D.
E.
F.
The current is constant and is
directed from a to b.
The current is constant and is
directed from b to a.
The current is increasing and
is directed from a to b.
The current is decreasing and
is directed from a to b.
The current is increasing and
is directed from b to a.
The current is decreasing and
is directed from b to a.
57%
28%
6%
2%
4% 4%
RL circuit
Chapter 32.2-4
Day 35
Exam 3
--- date : November 21, Monday at class.
--- Please remember your official section.
--- Materials covered : Chapter 29, 30, 31 and 32 of the textbook,
lectures, recitation materials, and homework 8-11.
--- Student ID & Black lead pencil (# 2 1/2 or softer)
--- No calculator, no phone, no laptop, no scratch papers are allowed
A coil with zero resistance has its ends labeled a and b.
The potential at a is higher than at b. Which of the
following could be consistent with this situation?
A.
B.
C.
D.
E.
F.
The current is constant and is
directed from a to b.
The current is constant and is
directed from b to a.
The current is increasing and
is directed from a to b.
The current is decreasing and
is directed from a to b.
The current is increasing and
is directed from b to a.
The current is decreasing and
is directed from b to a.
57%
28%
6%
2%
4% 4%
Consider the circuit in Figure with S1 open and S2 at position a.
switch S1 is now thrown closed. At the instant it is closed, across
which circuit element is the voltage equal to the emf of the
battery?
56%
33%
A.
B.
C.
the resistor
the inductor
both the inductor and
resistor
10%
Consider the circuit in Figure with S1 open and S2 at position a.
switch S1 is now thrown closed. After a very long time, across
which circuit element is the voltage equal to the emf of the
battery?
63%
35%
A.
B.
C.
the resistor
the inductor
both the inductor and
resistor
2%
RL circuit
RL circuit with battery
dI
ε IR L
0
dt
ε
I
1  e Rt L
R


RL circuit without battery
An inductor produces a back emf in a DC series RL
circuit when a switch connecting the battery to the
circuit is closed. We can explain this by
A.
B.
C.
D.
E.
Lenz’s law.
increasing magnetic flux within
the coils of the inductor.
increasing current in the coils
of the inductor.
all of the above.
only (1) and (3) above.
93%
1%
3%
2%
2%
When a switch is closed to complete a DC series RL
circuit with a battery,
A.
B.
C.
D.
E.
the electric field in the wires
increases to a maximum value.
the magnetic field outside the wires
increases to a maximum value.
the rate of change of the electric
and magnetic fields is greatest at
the instant when the switch is
closed.
all of the above are true.
only (1) and (3) above are true.
83%
9%
1%
3%
4%
32.3 Energy (density) stored in Magnetic field
dU
dI
 LI
dt
dt
1 2
U  L  I d I  LI
0
2
U B2
uB  
V 2 μo
I
Energy stored in solenoid
2
1
B2
2  B 
U  μo n V 
V
 
2
2μo
 μo n 
Chapter 32.4-6
Day 36
Exam 3
--- On Monday, 11/21, during the class
--- Practice exam sometime on Thursday, 11/17
--- Review on this Friday, 11/18
A coil with zero resistance has its ends labeled a and b.
The potential at a is higher than at b. Which of the
following could be consistent with this situation?
A.
B.
C.
D.
E.
F.
The current is constant and is
directed from a to b.
The current is constant and is
directed from b to a.
The current is increasing and
is directed from a to b.
The current is decreasing and
is directed from a to b.
The current is increasing and
is directed from b to a.
The current is decreasing and
is directed from b to a.
57%
28%
6%
2%
4% 4%
RL circuit
RL circuit with battery
a
b
Current is clockwise from a to b, increasing. Potential
is supplied by the battery (bigger) and inductor
(smaller), Va is higher than Vb.
RL circuit without battery
b
a
Current is clockwise from b to a , decreasing.
Only potential is supplied by the inductor, Va is
higher than Vb.
32.4 Mutual inductance
d 12
d I1
ε2  N2
 M12
dt
dt
d I2
ε1  M21
dt
M12 = M21 = M
Example of Mutual inductance
32.5 LC circuit
Q = Qmax cos (ωt + φ), ω  1
dQ
I
 ωQmax sin(ωt  φ )
dt
LC
Q2 1 2
U  UC  UL 
 LI
2C 2
32.6 RLC circuit
2
dQ
dQ Q
L 2 R
 0
dt
dt C
-- special cases with L=0, or R=0, or C=0.
Analogies Between Electrical and Mechanic Systems
R = 0, circuit reduces to an LC circuit (no damping)
Small R, light damping with (ω : angular frequency)
Q = Qmax
e-Rt/2L
cos ωt,
 1 R  
ωd  

 
LC
2
L

 

R = RC  4L / C , the circuit is critically damped.
R > RC, the circuit is said to be overdamped.
2
1
2