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Physics
ys cs 132:
3 Lecture
ectu e 21
Elements of Physics II
A
Agenda
d for
f T
Today
d


Induced EMF
 Force on moving charges
 Induced Current
Magnetic Flux
 Area Vector
Physics 201: Lecture 1, Pg 1
Clicker Question 11:
A rectangular loop of wire is carrying current as shown. There is a
uniform magnetic field parallel to the sides ab and cd.
The loop will:
(a) move to the right
(b) move to the left
(c) move up
(d) move down
(e) rotate
B
d
a
c
b
Physics 201: Lecture 1, Pg 2
Atomic Magnets
 A plausible explanation for
the magnetic properties of
materials is the orbital motion
of the atomic electrons.
 The figure shows a simple
simple,
classical model of an atom in
which a negative
g
electron
orbits a positive nucleus.
 In this picture of the atom, the electron’s motion is that
of a current loop!
 An orbiting electron acts as a tiny magnetic dipole,
with a north pole and a south pole
pole.
Physics 201: Lecture 1, Pg 3
Magnetic Effects of Electrons – Spins

Electrons also have spin
 The classical model is to
consider
id th
the electrons
l t
tto spin
i
like tops
 It is actuallyy a q
quantum effect
Physics 201: Lecture 1, Pg 4
Magnetic Properties of Matter
 For most elements, the
magnetic moments of
th atoms
the
t
are
randomly arranged
when the atoms join
together to form a
solid.
 As the figure shows,
this random
arrangement produces
a solid whose net
magnetic moment is
very close to zero.
Physics 201: Lecture 1, Pg 5
Ferromagnetism
 In iron, and a few
other substances, the
atomic magnetic
moments tend to all
line up in the same
direction, as shown
in the figure.
g
 Materials that behave
in this fashion are
called ferromagnetic,
with the prefix ferro
meaning “iron-like
iron like.”
Physics 201: Lecture 1, Pg 6
Ferromagnetism
 A typical piece of iron is divided
into small regions, typically less
than 100 m in size, called
magnetic domains.
 The magnetic moments of all
the iron atoms within each
domain are perfectly aligned
aligned,
so each individual domain is
a strong magnet.
 However, the various magnetic
domains that form a larger solid
are randomly
d l arranged.
d
Physics 201: Lecture 1, Pg 7
Physics 201: Lecture 1, Pg 8
Induced Magnetic Dipole
 If a ferromagnetic substance is subjected to an external
magnetic field
field, the external field exerts a torque on the
magnetic dipole of each domain.
q causes
 The torque
many of the domains
to rotate and become
aligned
li
d with
ith th
the
external field.
Physics 201: Lecture 1, Pg 9
Review RHR

Flat RHR
 Direction of force
charge/current moving in B
field?
Out of page
+ + + +
v
 Curly RHR #1
 Curly RHR #2
 Direction of B-field from
loop of wire?
 Direction of B-field from
wire? CCW
Out of page
•
Physics 201: Lecture 1, Pg 10
So far

Moving charges create B
B-fields
fields (cause magnets)
 Atomic level: electrons cause magnetism
 Cu
Current
e in a wire
e

B-fields exert forces on moving charges
 Current carrying wire feels a force

Now: change in B-field causes moving charges!!!
Physics 201: Lecture 1, Pg 11
Faraday’s Law


Key to EVERYTHING in E+M
 Generating electricity
 Microphones,
c op o es, Spea
Speakers
esa
and
d Tape
ape Decks
ec s
 Amplifiers
 Electric Guitars
Changing B-field creates E-field
Physics 201: Lecture 1, Pg 12
Faraday’s Discovery of 1831

When a bar magnet is pushed
into a coil of wire, it causes a
momentary deflection of the
current-meter needle.

A quick withdrawal of the
magnet deflects the needle in
the other direction.

Holding the magnet inside the
coilil h
has no effect.
ff t
Physics 201: Lecture 1, Pg 13
Motional EMF
Physics 201: Lecture 1, Pg 14
Motional EMF
Physics 201: Lecture 1, Pg 15
Motional EMF
Physics 201: Lecture 1, Pg 16
Motional EMF
 The magnetic force
g carriers
on the charge
in a moving conductor
creates an electric field of
strength E = vB inside the
conductor.
 For a conductor of
length l, the motional
emf perpendicular to
the magnetic
g
field is:
Physics 201: Lecture 1, Pg 17
Clicker Question 1:
A metal bar moves through a
magnetic field
field. The induced
charges on the bar are
Physics 201: Lecture 1, Pg 18
Induced Current

If we slide a conducting
wire along a U-shaped
conducting rail, we can
complete a circuit and drive
an electric current.

If the total resistance of the
circuit is R, the induced
currentt is
i given
i
b
by Oh
Ohm’s
’
law as:
Physics 201: Lecture 1, Pg 19
Induced Current
 The figure shows a
conducting wire sliding
to the left.
left
 In this case, a pushing
force is needed to keep
the wire moving at
constant speed.
 Once again
again, this input
power is dissipated in
the electric circuit.
 A device that converts
mechanical energy to
electric energy is called
a generator.
Physics 201: Lecture 1, Pg 20
Clicker Question 2:
A metal
e a bar
ba o
of length
e g 1.5
5 m is
s pu
pulled
ed a
along
o g a track
ac a
at a
velocity of 4 m/s. A magnetic field of 2 T points into
the page. What current flows through the 2 
resistor?
(a) 12 Amps
(b) 6 Amps
(c) 2 Amps
(d) 24 Amps
(e) 3 Amps
Physics 201: Lecture 1, Pg 21
Clicker Question 3:
A metal
e a bar
ba o
of length
e g 1.5
5 m is
s pu
pulled
ed a
along
o g a track
ac a
at a
velocity of 4 m/s. A magnetic field of 2 T points into
the page. What direction does the current flow
through the resistor?
(a) Top to bottom
(b) Bottom to top
Physics 201: Lecture 1, Pg 22
Eddy Currents
 Consider pulling a sheet of
metal through a magnetic field.
 Two “whirlpools” of current
begin to circulate in the solid
metal called eddy currents.
metal,
currents
 The magnetic force on the
eddy currents is a retarding
force.
 This is a form of magnetic
braking.
braking
Physics 201: Lecture 1, Pg 23
Magnetic Flux

Number of B
B-field
field lines that pass through a
surface
B
A uniform magnetic field, B, passes through a
plane surface of area A.
Magnetic flux   B A
B
Magnetic flux   B A cos()

Note: The flux can be negative!
Physics 201: Lecture 1, Pg 24
Magnetic Flux
The magnetic flux
measures the amount of
magnetic field passing
through a loop of area A if
the loop is tilted at an angle
 from the field.
The SI unit of magnetic flux is the weber:
1 weber = 1 Wb = 1 T m2
Physics 201: Lecture 1, Pg 25
The Area Vector
 Let’s define an area vector
to be a vector in
the direction of,
of perpendicular to the surface
surface, with a
magnitude A equal to the area of the surface.
 Vector
has units of m2.
Physics 201: Lecture 1, Pg 26
Magnetic Flux Through a Loop
Physics 201: Lecture 1, Pg 27
Clicker Question 4:
The metal loop is being pulled through a uniform
magnetic field. Is the magnetic flux through
the loop changing?
A. Yes.
B No.
B.
No
Physics 201: Lecture 1, Pg 28
Clicker Question 5:
The metal loop is being pulled through a uniform
magnetic field. Is the magnetic flux through
the loop changing?
A. Yes.
B No.
B.
No
Physics 201: Lecture 1, Pg 29
Clicker Question 6:
A conducting
g rod is sliding
g at a velocity
y v = 0.12 m/s on
conducting rails. At time t = 0 the rod is at position l = 0.5 m (see
picture). The entire device is placed in a uniform magnetic field B
= 0.45 T directed into the page. The width w = 0.4 m. What is
the magnetic flux Φ through the conducting loop at time t = 0 ?
(a)
(b)
(c)
(d)
(e)
Φ = 0 T-m2
Φ = 0.09 T-m2
Φ = 0.198 T-m2
Φ = 0.45 T-m2
Φ = 12 T-m2
Physics 201: Lecture 1, Pg 30
Clicker Question 7:
A loop of wire of area A is tipped at an angle  to a uniform magnetic field B.
The maximum flux occurs for an angle  = 0 . What angle  will give a flux
that is ½ of this maximum value?
A.
A
B.
C.
D
D.
  30
  45
  60
  90
Physics 201: Lecture 1, Pg 31
Lenz’s Law
Physics 201: Lecture 1, Pg 32
Lenz’s Law
 Pushing the bar magnet
into the loop causes the
magnetic flux to increase
in the downward direction.
 To oppose the change in
flux, which is what Lenz’s
law requires, the loop
it lf needs
itself
d tto generate
t
an upward-pointing
g
field.
magnetic
 The induced current
ceases as soon as the
magnet stops moving.
Physics 201: Lecture 1, Pg 33
Lenz’s Law
 Pushing the bar magnet away from the loop causes the
magnetic flux to decrease in the downward direction.
 To oppose this decrease, a clockwise current is induced.
Physics 201: Lecture 1, Pg 34
Clicker Question 8:
A magnetic field goes through a loop of wire, as below. If the
magnitude of the magnetic field is increasing, what can we say
about
b t th
the currentt in
i the
th loop?
l
?
A. The loop has a clockwise current.
B. The loop has a counterclockwise current.
C. The loop has no current.
Physics 201: Lecture 1, Pg 35
Clicker Question 9:
A magnetic field goes through a loop of wire, as below. If the
magnitude of the magnetic field is decreasing, what can we say
about
b t th
the currentt in
i the
th loop?
l
?
A. The loop has a clockwise current.
B. The loop has a counterclockwise current.
C. The loop has no current.
Physics 201: Lecture 1, Pg 36
Clicker Question 10:
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 37
Clicker Question 11:
A conducting rod slides
on a conducting
g track in a
constant B field directed
into the page. What is
the direction of the
x x x x x x x x x x x
induced current?
x x x x x x x x x x x
a) clockwise
x x x x x x x x x x x
v
x x x x x x x x x x x
b) counterclockwise
c) no induced current
Physics 201: Lecture 1, Pg 38