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
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 3
Clicker Question 1:
The magnetic field
f
points out off the page and is increasing.
(a) The current will flow counterclockwise.
(b) The current will flow clockwise.
(c) There will be no current.
Physics 201: Lecture 1, Pg 4
Clicker Question 2:
The magnetic field
f
points out off the page and is decreasing.
(a) The current will flow counterclockwise.
(b) The current will flow clockwise.
(c) There will be no current.
Physics 201: Lecture 1, Pg 5
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 6
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 7
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 8
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 9
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 10
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 11
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 12
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 13
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 14
Example:
A 4 cm × 3 cm rectangular loop is made of a wire 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?
Physics 201: Lecture 1, Pg 15
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 16
Example:
A circular loop of radius r = 5 cm and resistance R =
0.10 Ω is in a region
g
where there is a uniform
magnetic field in the direction shown in the figure
that increases linearly with time according to the
expression
p
B(t)
( ) = B0 t / τ with B0 = 0.5 T and τ =
100 s. (The loop is stationary.)
What is the magnitude of the
induced current in the loop?
p
(a) I = 0
(b) I = 0.34 mA
(c) I = 0.39 mA
(d) I = 0.2 mA
(e) I = 3.4A
Physics 201: Lecture 1, Pg 17
Example:
A circular loop
p of radius r = 5 cm and resistance R = 0.10 Ω is in a
region where there is a uniform magnetic field in the direction
shown in the figure that increases linearly with time according
p
B(t)
( ) = B0 t / τ with B0 = 0.5 T and τ = 100 s.
to the expression
(The loop is stationary.)
Physics 201: Lecture 1, Pg 18
Clicker Question 10:

A circular loop of radius r = 5 cm and resistance R =
0 10 Ω is in a region where there is a uniform
0.10
magnetic field in the direction shown in the figure
that increases linearly with time according to the
expression B(t) = B0 t / τ with B0 = 0.5
0 5 T and τ =
100 s. (The loop is stationary.)
What direction will current
fl
flow
iin th
the lloop?
?
(a)
(b)
Physics 201: Lecture 1, Pg 19
Induced Fields
Physics 201: Lecture 1, Pg 20
Maxwell’s Theory of Electromagnetic Waves

A changing electric field
creates a magnetic field,
field
which then changes in just
the right way to recreate the
electric
field, which then changes in
just the right way to again
recreate the
h magnetic
i fifield,
ld
and
so on.

This is an electromagnetic
wave.
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