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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
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 2
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 3
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 4
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 5
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 6
Physics 201: Lecture 1, Pg 7
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 8
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 9
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 10
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 11
Motional EMF
Physics 201: Lecture 1, Pg 12
Motional EMF
Physics 201: Lecture 1, Pg 13
Motional EMF
Physics 201: Lecture 1, Pg 14
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 15
Clicker Question 1:
A metal bar moves through a
magnetic field
field. The induced
charges on the bar are
Physics 201: Lecture 1, Pg 16
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 17
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 18
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 19
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 20
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 21
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 22
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 23
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 24
Magnetic Flux Through a Loop
Physics 201: Lecture 1, Pg 25
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 26
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 27
Clicker Question 7.5:
The following figure shows a 2.0 cm diameter solenoid passing through the
center of a 7.0 cm diameter loop. The magnetic field inside the solenoid is
0.20 T. In which case is the flux through the loop greater?
A.
B.
C
C.
They are the same
Physics 201: Lecture 1, Pg 28
Pre-Class Quiz
The following figure shows a 2.0 cm diameter solenoid
passing through the center of a 7.0 cm diameter loop. The
magnetic
g
field inside the solenoid is 0.20 T. What is the
magnetic flux through the loop when it is perpendicular to
the solenoid?
5
6.3  10 Wb
Physics 201: Lecture 1, Pg 29
Pre-Class Quiz
The following figure shows a 2.0 cm diameter solenoid
passing through the center of a 7.0 cm diameter loop. The
magnetic
g
field inside the solenoid is 0.20 T. What is the
magnetic flux through the loop when it is tilted at a 60°
angle?
Physics 201: Lecture 1, Pg 30