Physics
ys cs 132:
3 Lecture
ectu e 22
Elements of Physics II
A
Agenda
d for
f T
Today
d


Lenz’ Law
 Emf opposes change in flux
Faraday’s Law
 Induced EMF in a conducting loop
Physics 201: Lecture 1, Pg 1
Lenz’s Law
Physics 201: Lecture 1, Pg 2
Lenz’s Law

Why?

Does lenz
lenz's
s law apply to the moment of the change in flux or
will the induced B field be the "permanent" field after the
change.
Physics 201: Lecture 1, Pg 3
Lenz’s Law
Reasoning Strategy
1.
Find the direction of the magnetic flux that penetrates the coil.
2.
Determine whether the magnetic flux that penetrates the coil is
increasing or decreasing.
 Increasing: induced b-field opposes magnetic flux
 Decreasing: induced b-field aligned with magnetic flux
3.
Use RHR-2 to determine the direction of the induced current.
Physics 201: Lecture 1, Pg 4
Clicker Question 1:
The magnetic field
f
points out off the page and is increasing.
(a) The induced current will flow counterclockwise.
(b) The induced current will flow clockwise.
(c) There will be no induced current.
Physics 201: Lecture 1, Pg 5
Clicker Question 1:
Correct: “The
The loop creates an induced magnetic field opposite of
the actual magnetic field to keep the magnetic flux constant.
Since the induced field points into the page, the current will
flow clockwise because of the right hand rule
rule.”
“The change in flux is increasing out of the page, so by the righthand rule a clock-wise current is needed to induce a magnetic
field pointing into the page.”
“When the magnetic field is increasing the induced field of the
induced current is pointing in the opposite direction of the
magnetic field. I used the curly right hand rule : thumb points in
direction of induced magnetic field and fingers curl in direction
of induced current
current. “
“Science”
Incorrect: “The external magnetic
g
field p
points out, the induced field
must always counteract this field and point in.”
Physics 201: Lecture 1, Pg 6
Clicker Question 2:
The magnetic field
f
points out off the page and is decreasing.
(a) The induced current will flow counterclockwise.
(b) The induced current will flow clockwise.
(c) There will be no induced current.
Physics 201: Lecture 1, Pg 7
Clicker Question 3:
The two loops off wire in the figure
f
are stacked one above the
other. Does the upper loop have a clockwise current (from
above), a counterclockwise current, or no current at the
following times? Before the switch is closed.
(a) The current will flow counterclockwise.
(b) The current will flow clockwise
clockwise.
(c) There will be no current.
Physics 201: Lecture 1, Pg 8
Clicker Question 4:
The two loops off wire in the figure
f
are stacked one above the
other. Does the upper loop have a clockwise current (from
above), a counterclockwise current, or no current at the
following times? Immediately after the switch is closed.
(a) The current will flow counterclockwise.
(b) The current will flow clockwise
clockwise.
(c) There will be no current.
Physics 201: Lecture 1, Pg 9
Clicker Question 5:
The two loops off wire in the figure
f
are stacked one above the
other. Does the upper loop have a clockwise current (from
above), a counterclockwise current, or no current at the
following times? Long after the switch is closed.
(a) The current will flow counterclockwise.
(b) The current will flow clockwise
clockwise.
(c) There will be no current.
Physics 201: Lecture 1, Pg 10
Clicker Question 6:
The two loops off wire in the figure
f
are stacked one above the
other. Does the upper loop have a clockwise current (from
above), a counterclockwise current, or no current at the
following times? Immediately after the switch is reopened.
(a) The current will flow counterclockwise.
(b) The current will flow clockwise
clockwise.
(c) There will be no current.
Physics 201: Lecture 1, Pg 11
Example:
The bar magnet is pushed
toward the center of a wire loop.
Which is true?
A.
There is a clockwise induced
current in the loop.
B.
There is a counterclockwise
induced current in the loop.
C.
There is no induced current in the
loop.
p
Physics 201: Lecture 1, Pg 12
Clicker Question 7:

A ccircular
cu a co
conducting
duc g loop
oop is
s be
being
g moved
o ed up
upward
ad
(toward a current-carrying wire) at a constant
speed. What will be the direction of the induced
current?
(a) No current will be induced (no flux change).
(b) Current will be induced clockwise.
(c) Current will be induced counter
counter-clockwise.
clockwise
Physics 201: Lecture 1, Pg 13
Clicker Question 8:
If a coil is rotated as shown, in a magnetic field
pointing
p
g to the left,, in what direction is the induced
current?
a) clockwise
b) counterclockwise
c) no induced current
Physics 201: Lecture 1, Pg 14
Faraday’s Law

An emf is induced in a conducting loop if the
magnetic flux through the loop changes
changes.

The magnitude of the emf is:

The direction of the emf is such as to drive an
induced current in the direction given by Lenz’s
law.
Physics 201: Lecture 1, Pg 15
Using Faraday’s Law

If we slide a conducting
wire along a U-shaped
conducting rail, we can
complete a circuit and
drive an electric current.

We can find the induced
emf and current by using
F d ’ llaw and
Faraday’s
d Oh
Ohm’s
’
law:
Physics 201: Lecture 1, Pg 16
Example:
A 4 ccm × 3 ccm rectangular
ec a gu a loop
oop is
s made
ade o
of a wire
e with
resistance of 3.5 Ohm. The loop is placed in a
region of uniform magnetic field, B = 5 T. The
direction of B is perpendicular to the plane of the
loop and points into the page as shown. The
magnetic field starts to increase at a uniform rate of
0.1 T/sec. What is the magnitude of the induced
current in the loop?
(a) I = 0 A
(b) I = 3.4
3 4 × 10-55 A
(c) I = 1.2 × 10-4 A
(d) I = 0.02 A
(e) I = 4.8
48A
Physics 201: Lecture 1, Pg 17
Example:
A 4 cm × 3 cm rectangular loop is made of a wire with resistance
off 3.5
3 5 Ohm.
Oh The
Th loop
l
iis placed
l
d iin a region
i off uniform
if
magnetic
ti
field, B = 5 T. The direction of B is perpendicular to the plane of
the loop and points into the page as shown. The magnetic field
starts
t t to
t increase
i
att a uniform
if
rate
t off 0.1
0 1 T/sec.
T/
What
Wh t is
i the
th
magnitude of the induced current in the loop?
Physics 201: Lecture 1, Pg 18
Clicker Question 9:

A 4 ccm × 3 ccm rectangular
ec a gu a loop
oop is
s made
ade o
of a wire
e
with resistance of 25 Ohm/m. The loop is placed in
a region of uniform magnetic field, B = 5 T. The
direction of B is perpendicular to the plane of the
loop and points into the page as shown. The
magnetic field starts to increase at a uniform rate of
0.1 T/sec. What is the direction of the induced
current?
(a) counterclockwise
(b) clockwise
(c) There is no induced
current.
Physics 201: Lecture 1, Pg 19
Example:

A solenoid with cross sectional area A = 4 × 10-4 m2
is 0
0.120
120 m long and has 2500 turns
turns. The magnetic
field at the center of the solenoid is 5 × 10-3 T
pointing into the page. A square wire loop 1.5 cm
on each side is fixed inside the solenoid as shown
shown.
The current in the solenoid is uniformly decreased
to zero over 10 seconds. What is the magnitude of
the induced emf in the square loop?
(a) 1.125 × 10-7 V
(b) 1.259 × 10-7 V
(c) 2.124 × 10-7 V
(d) 2.486 × 10-6 V
((e)) 1.124 × 10-6 V
Direction?
CW
Physics 201: Lecture 1, Pg 20
Example:

A solenoid with cross sectional area A = 4 × 10-4 m2 is 0.120 m
l
long
and
dh
has 2500 tturns. The
Th magnetic
ti field
fi ld att th
the center
t off th
the
solenoid is 5 × 10-3 T pointing into the page. A square wire loop
1.5 cm on each side is fixed inside the solenoid as shown. The
currentt in
i the
th solenoid
l
id iis uniformly
if
l d
decreased
d tto zero over 10
seconds. What is the magnitude of the induced emf in the
square loop?
Physics 201: Lecture 1, Pg 21
Applications of Faraday’s
Faraday s Law –
Electric Guitar




A vibrating string induces an
emf in a coil
Ap
permanent magnet
g
inside
the coil magnetizes a portion
of the string nearest the coil
As the string vibrates at some
frequency, its magnetized
segment produces a
changing flux through the
pickup coil
The changing flux produces
an induced emf that is fed to
p
an amplifier
Physics 201: Lecture 1, Pg 22
Applications of Faraday’s
Faraday s Law –
Microphone
Physics 201: Lecture 1, Pg 23
Applications of Faraday’s
Faraday s Law – Apnea
Monitor



The coil of wire attached
to the chest carries an
alternating current
An induced emf produced
by the varying field passes
through
g ap
pick up
p coil
When breathing stops, the
pattern of induced
voltages
g stabilizes and
external monitors sound
an alert
Physics 201: Lecture 1, Pg 24