magnetism magnetism magnetism

MAGNETISM
MAGNETIC
INDUCTION AND
LENZ’ LAW
fluxgate magnetometer gradiometry in archeological geophysics:
source: http://www.geophysics.co.uk/archaeol.htm
Levitating superconductor:
Source: wikimedia
William Gilbert demonstrating
magnetic phenomena to Queen
Elizabeth I:
A video shot on the Rokko Liner in Kobe, Japan shows how
paperclips stand on end when the train accelerates and brakes.! The
magnetism is produced by the electric current that drives motors
located under the floor: source: http://www.flatrock.org.nz/
source: http://gallery.nen.gov.uk/
Induction Heating: Source: http://www.rdoent.com/electromagneticinduction.htm
Physics in-service day 2010
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MAGNETISM
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MAGNETISM
OUTLINE
•Electric force vs magnetic force.
•Current carrying wires and loops.
•Direction of force and right hand rule.
•Current loops and torque.
•Solenoids
•Electromagnetic Induction
•Lenz’ Law + demonstrations
•Faraday’s Law: an example from our Sensors subject.
•Levitation
•Ferro-fluidics
•Microprobes and Melbourne Trams
BACKGROUND:ELECTRIC FORCE
!"#$"%&'()*+,-)./,0'#123'4"516"7'&8$8792'4"'1:";'
4:84'%8<764#32'"='="592>'!>'&?;'4;"'9:85<21>''
(%8<764#3210'q1'873'q2>'61'<6@27'&AB
F = ke
q1 q2
Coulomb� s Law
r2
F
q2
q1
r
!"714874B
1
ke =
= 8.99 $10 9 Nm 2 /C 2
4 " #0
Electrostatic Levitator: Jan Rogers, NASA
Marshall Spaceflight Center
"0 = 8.85 #10$12 C 2 /Nm 2
( permittivity of free space)
!
!
BACKGROUND: MAGNETIC FORCE
BACKGROUND: MAGNETIC FORCE
A magnetic field exerts a force on a moving charge, given by:
! This is the force on test charge q which is
moving with velocity v.
! The magnetic force is always perpendicular
to
and , with a direction given by the
RH rule.
! Since F is perpendicular to v, magnetic
force cannot change the speed of the
charged particle.
(Fig 29-2: Fundamentals of Physics, 6th Ed., Halliday,
Resnick and Walker, John Wiley and sons, New York, 2001)
+ve charge
Fig 33.35 Physics for Scientists and Engineers, 2nd Ed., Randall Knight,
Pearson.
v
source: http://coe.kean.edu/~afonarev/Physics/Magnetism/
BACKGROUND: MAGNETIC FORCE
BACKGROUND: MAGNETIC FORCE
C:2'F8<72E9'G"592'"7'4;"'H"674'9:85<21B
C;"'%"@67<'9:85<21'2D254'%8<72E9'="5921'"7'289:'"4:25B
Two point charges, q2 & q1,
instantaneously moving side by side
with parallel velocities v1 & v2
Magnetic force on q1 :
Fig 33.35 Physics for Scientists and Engineers, 2nd Ed., Randall Knight,
Pearson.
(attractive if q1, q2 same sign and v1, v2 parallel)
(zero if v1 or v2 = 0)
(This force acts in addition to electric force)
F =
BACKGROUND: MAGNETIC FORCE
C:2'F8<72E9'G"592'"7'4;"'H"674'9:85<21B
BACKGROUND: MAGNETIC FORCE
C:2'F8<72E9'G"592'"7'4;"'H"674'9:85<21B
General case:
Force vectors:
!In general, these force vectors not equal and opposite ! Newton's 3rd law
appears to be violated.
!Momentum conservation requires inclusion of momentum associated with
moving E-field (E-field moving with each charge). ( E-field has energy
density associated with it and moving energy distribution has momentum.)
1 q1 q2
Coulomb� s Law
4π�0 r2
BACKGROUND: FORCE ON CURRENT
CARRYING WIRE:
BACKGROUND: FORCE ON CURRENT
CARRYING WIRE:
Force on dq in segment dl is:
MIT Physics Demo -- Jumping Wire
source: http://coe.kean.edu/~afonarev/Physics/Magnetism/
TORQUE ON CURRENT LOOP: DC
MOTOR:
http://www.youtube.com/watch?v=tUCtCYty-ns&feature=channel
TORQUE ON CURRENT LOOP:
Torque
�
µ×B
Potential energy: U = −�
µ
(Figs 29-20, 29-21 Fundamentals of Physics,
6th Ed., Halliday, Resnick and Walker, John
Wiley and sons, New York, 2001)
•
Ffront and Fback cancel.
• Ftop and Fbottom don’t act along same line
! they rotate the loop by exerting a torque.
Use the right hand curl rule to find
direction of µ.
i
http://www.euclideanspace.com/
RH curl rule for direction of B-field
associated with current i in wire:
(Figs 30-2, 30-3, 30-4: Fundamentals of Physics, 6th
Ed., Halliday, Resnick and Walker, John Wiley and
sons, New York, 2001)
BACKGROUND: FORCE ON CURRENT
CARRYING WIRE:
BACKGROUND: FORCE ON CURRENT
CARRYING WIRE:
MIT Physics Demo -- Forces on a Current-Carrying Wire
http://www.youtube.com/watch?v=43AeuDvWc0k&feature=related
F8<72E9'I2$3'$6721'"='8'9659#$85'9#55274'$""H'852'$6J2'
4:84'"='8'&85'%8<724B
i
F
i
B
MIT Physics Demo -- Forces on a Current-Carrying Wire
http://www.youtube.com/watch?v=43AeuDvWc0k&feature=related
(Fig 30-21: Fundamentals of Physics, 6th Ed., Halliday,
Resnick and Walker, John Wiley and sons, New York, 2001)
C:2'F8<72E9'K6H"$2'-'(!#55274'L""H0B
Electrons, protons and many other elementary particles have
magnetic dipole moments.
At large distances, B-field line
distribution of current loop reminiscent
of E-field pattern of electric dipole.
For large distance:
µe = 9.34 × 10−24 Am2
(They behave like tiny "quantum" current loops)
Earth has magnetic dipole moment:
µEarth = 8.00 × 1022 Am2
Magnetic Dipole Moment:
µB = iπR2
= i × loop area
(Correct for plane loop of arbitrary shape since arbitrary loop can be
composed from many small circular loops)
M"$27"63B'N2@62;
A solenoid is a conducting wire wound in tight
helical coil with current i flowing through it.
B-field distribution similar to
that of stack of individual
rings each carrying current i .
B-field strong inside solenoid but relatively weak outside.
B-field pattern for loosely
wound solenoid:
(Figs 30-16, 30-17: Fundamentals
of Physics, 6th Ed., Halliday,
Resnick and Walker, John Wiley
and sons, New York, 2001)
Solenoids are used to create uniform magnetic fields.
(Compare with the electric field of a parallel plate
capacitor.
P$2945"%8<72E9'Q73#9E"7B
O'1"$27"63'61'87'2$2945"%8<724B
A changing magnetic field generates an "induced electric
field".
Michael Faraday: English physicist (1791-1867) discovered
this phenomenon and formulated the relationship b/w the
rate of change of the B-field and the induced E-field (+
induced emf).
The electric field outside of a solenoid looks like that of a bar
magnet. Use RH rule to identify the north pole. A solenoid with
many turns and a large current is a powerful magnet.
Faraday's experiment showing induction between coils of wire:
source: wikipedia
F"E"78$'2%=B
Induced emf = lE
= vlB
Move metal rod through uniform
magnetic field at velocity
Free charges experience magnetic
force
-
−ve charges move to the bottom
of rod, creating an electric field in
the conductor.
Net movement of charges until the
electric field generated balances
magnetic force:
+
Equilibrium:
e's
Fig 34.2 Physics for Scientists and Engineers, 2nd Ed.,
Randall Knight, Pearson.
The motional emf of a
conductor of length l moving
with velocity v perpendicular
to a magnetic field B is:
Fig 34.2 Physics for Scientists and Engineers, 2nd Ed.,
Randall Knight, Pearson.
F8<72E9'G$#D'!B'B
Q73#923'9#55274B
Magnetic flux "B through surface:
Now include the moving conductor
in a circuit, allowing a flow of
current.
The induced current is given by:
ΦB =
Units:
where R is the resistance of the
circuit.
Fig 34.5 Physics for Scientists and Engineers, 2nd Ed.,
Randall Knight, Pearson.
Need to apply a force (pull the wire) to keep it moving
at constant speed. Mechanical work ! electric energy
(dissipated as i2R heating in circuit).
�
� A
�
B.d
� A
�
dΦB = B.d
( # of field lines through surface)
1 Wb (weber) = 1 T.m2
Change in flux through loop as rod
moves:
� A
� = Bldx
dΦB = B.d
Rate of change is:
dx
dΦB
= Bl
= Blv = �emf
dt
dt
Fig 34.5 Physics for Scientists and Engineers, 2nd Ed.,
Randall Knight, Pearson.
(we will worry about the sign later)
P33A'9#552741B
P33A'9#552741B
When loop is pulled through a B-field
region, a current is induced in the loop.
A force must be exerted to pull the loop
out ! mechanical energy is dissipated as
thermal energy (i2R heating) in circuit.
Solid conducting plate moved through
field ! same direction for induced
current but e's not constrained by
boundaries of wire ! many current
loops formed (eddy currents) in plate.
Energy dissipated by i2R heating in plate.
Can slot plate to inhibit eddy current
formation.
Fig 34.9 & 34.10 Physics for Scientists and Engineers, 2nd
Ed., Randall Knight, Pearson.
source: http://demoroom.physics.ncsu.edu/html/demos/163.html
O7"4:25';8A'"='673#967<'87'2%=B
Move magnet toward loop:
! increasing # of B-field lines
intercept surface enclosed by loop
! changing "B
! current induced in loop.
Direction of current opposes
change in field.
L27RS1'L8;B
There is an induced current in a closed, conducting loop if
and only if the magnetic flux through the loop is changing.
The direction of the induced current is such that the induced
magnetic field opposes the change in the flux.
N
S
S
N
Induced i and direction of field due to current in loop
� A
�
dΦB = B.d
Fig 34.19 Physics for Scientists and Engineers, 2nd Ed.,
Randall Knight, Pearson.
Fig 34.20 Physics for Scientists and
Engineers, 2nd Ed., Randall Knight,
Pearson.
Induced i and direction of field due to current in loop
L27RS1'L8;B
L27RS1'L8;B
There is an induced current in a closed, conducting loop if
and only if the magnetic flux through the loop is changing.
The direction of the induced current is such that the induced
magnetic field opposes the change in the flux.
N
S
S
N
Fig 34.19 & 34.21 Physics for Scientists and Engineers,
2nd Ed., Randall Knight, Pearson.
source: http://www.youtube.com/watch?v=kU6NSh7hr7Q&feature=related
P33A'!#552741B'F8<724'67'O$'"5'!#'4#&2B
L27RS1'L8;B
S
N
N
S
Fig 34.19 Physics for Scientists and Engineers, 2nd Ed.,
Randall Knight, Pearson.
source: http://www.youtube.com/watch?v=nrw-i5Ku0mI
L27RS1'L8;B'T#%H67<'N67<1B
L27RS1'L8;B
MIT: Physics Demo -- Jumping Ring
source: http://www.youtube.com/watch?v=Pl7KyVIJ1iE&feature=related
source: http://www.youtube.com/watch?v=bkSsgTQOXVI
G85838AS1'L8;B
G85838AS1'L8;B
An emf is induced in a conducting loop if the magnetic
flux through the loop changes. The emf is given by
�=−
dΦB
dt
� A
�
dΦB = B.d
and the direction of the emf is such as to drive an
induced current in the direction given by Lenz’s law.
i.e. Induced emf is the rate of change of the magnetic
flux through the loop.
For coil of N turns:
� = −N
dΦper coil
dt
source: http://www.youtube.com/watch?v=GC9Hklor5bw
G85838AS1'L8;B
N"48E7<'L""H'F8<724"%2425B
Induced emf is the rate of change of the magnetic
flux through the loop.
dΦ
�=−
An instrument (now obsolete) for measuring magnetic
fields with high sensitivity:
B
dΦper coil
dt
� = −N
dt
© 1967 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material
for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers
or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
IEEE
TRANSACTIONS
ROTATING
COIL
478
A TURBINE
DRIVEN
ON NUCLEAR
SCIENCE,
JUNE
� A
�
dΦB = B.d
1967
MAGNETOMETER*
E. M. Rowe,
J. W. Hicks,
and G. E. Bush”‘”
Midwestern
Universities
Research
Association
Stoughton,
Wisconsin
Rotating loop in
static magnetic
field is another
way to induce
emf
Magnetometer
Summary
The first
step in the development
of this
A rotating
coil magnetometer
which
PHYC30013
Principles
and Applications
of Sensors,
2010:
device
was to employ
an air-driven
turbine
to
utilizes
an air turbine
to turn the coil has been
developed.
Since the turbine
rotor
forms
the
mount for the coil,
there
are no shafts
or gears.
Thus,
this magnetometer
may be used to measure fields
in locations
inaccessible
to more
conventional
rotating
coil devices.
The precision
of the suspension
of the turbine
and the lack of
mechanical
vibration
make it possible
to measure transverse
field
components
of the order
of
one milligauss
in a field
of one kilogauss.
The
sensitivity
of the magnetometer
is made independent
of the rotational
speed of the coil
through
the use of an electronic
integrator.
The
coil and integrator
circuit
is used in conjunction
with another
system
which
allows
the determination of the direction
of the magnetic
field
being
measured
relative
to a predetermined
direction.
A rotating coil magnetometer consists of a coil with 1000 turns. The coil is 5
cm in diameter and is rotated at a frequency of 500 Hz about the axis
shown in the figure. In the presence of a 100 μT magnetic field in the
direction shown, find the emf generated in the coil.
A = πr2
Introduction
Rotating
a coil in a magnetic
field
has been
a standard
method
of measuring
static
magnetic
fields
for many years.
Devices
based on this
principle
are simple,
reliable,
and, if reasonable care is taken in their
design
and construction,
extremely
accurate.
There
are,
however,
some drawbacks
to this method.
Among
these
are the necessity
for accurate
control
of the
rotational
speed,
the requirement
that the drive
motor
be coupled
to the coil through
a shaft long
enough
so that the presence
of the motor
will
not
affect
the field being measured-on
large
cyclotrons
this can be troublesome-and,
for some
very
low field
applications,
quite exotic
brush
designs
to minimize
electrical
noise.
Further,
to measure
the transverse
components
of a
magnetic
field
requires,
in many
cases,
very
sophisticated
electrical
or mechanical
design.
We would
like to describe
here a field
measuring
device
employing
a rotating
coil in which
the
difficulties
just mentioned
have been overcome.
� A)
� each
(B.
loop
� A)
� each
⇒ (B.d
source: http://www.youtube.com/watch?v=bkSsgTQOXVI
By placing
the coil within
the
rotate
the coil.
turbine
rotor,
the need for coupling
shafts
and/or
gear trains
was eliminated.
Thus,
the device
In addition,
either
can be made very
compact.
longitudinal
or transverse
components
of a field
may be measured
by simply
choosing
the proper
orientation
for the coil axis.
Figure
1 shows
the coil and turbine
assembly.
The coil is
wound
on a ceramic
form
for dimensional
stability.
The proportions
of the coil follow
the
criteria
developed
by Laslett’
so that the coil
measures
the field
at its magnetic
center,
independent
of gradient
to second
order.
The turbine
rotor
is made of linen-loaded
bakelite.
It
rotates
on berylium-copper
ball bearings.
Signal
pick-off
is accomplished
through
a standard Airflyte
electronics
assembly
(their
type
B30143
slip rings
and A30167
brushes)
utilizing
gold alloy
brushes
and slip rings.
While
these
slip ring-brush
assemblies
possess
excellent
2 these are not crucial
to the
noise properties,
Not shown in this figure
is a photo
cell
design.
and mirror
system
which
gives
a pulse
once per
revolution
of the coil.
⇒ �emf = −N
“Work
performed
U. S. Atomic
under
the auspices
Energy
Commission.
of the
!t
= Bπr2 cos θ = Bπr2 cos ωt
loop
Since a rotating
coil does not measure
the
field
directly
but rather
gives
an output
signal
proportional
to the rate at which
the projected
cross-sectional
area of the coil on the magnetic
field
varies
with time,
the output
signal
of any
rotating
coil device
will
depend not only on the
magnetic
field
but also the rotational
speed of
the coil.
It is unlikely
that a turbine
for this
application
can be built
that would
have the speed
regulation
of a good synchronous
motor
supplied
by a crystal-controlled
oscillator.
On the other
hand,
extremely
high gain operational
amplifiers
have been available
for some years.
By connecting one of these in integrator
configuration
to the
coil output,
the output
of the coil-integrator
circuit
can be made closely
proportional
to the
flux cut by the coil over a range
of speeds
given
= −ωBπr2 sin ωtdt
dΦ
= N ωBπr2 sin ωt = (620 mV) sin "t
dt
::c::
‘Now at the Lawrence
Radiation
Laboratory,
University
of California,
Livermore,
California.
B
by
107T
-<Wl
7
7TR
G
(1)
cf. Earth’s magnetic
field: 30 ! 60 µT
F8<72E9'G62$31'67'5212859:UB
source: http://www.youtube.com/watch?v=cEC9G8JUKW8
F8<72E9'G62$31'67'5212859:UB
source: http://www.youtube.com/watch?v=A1vyB-O5i6E
K68%8<72E9'L2@648E"7B
source: http://www.youtube.com/watch?v=m-Al7GAnH8Q&feature=related
These structures
were created by
the action of rare
earth magnets on a
liquid suspension of
magnetic particles
(a ferrofluid).
A movie of ferrofluid reacting to a magnetic field from an
electromagnet.
F8<72E9'G62$31'67'"#5'5212859:B'F2$&"#572'%695"H5"&2B
Luke28OR Ferrofluid demonstration, electromagnets power controlled by sound: source:http://
www.youtube.com/watch?v=zpBxCnHU8Ao
F8<72E9'G62$31'67'"#5'5212859:B
F2$&"#572'C58%1'67'"#5'5212859:B
x-ray detector
From accelerator
Scanner
Beam steerer &
Object collimators
1m
Aperture collimators
Probe forming lens
Microscope
RBS detector
Sample stage
goniometer
Low vibration
mounting
Ion pumps
Melbourne microprobe image showing effect of Tram Superstop
in Swanston St on microbeam stability in Physics basement. (We
moved beamline to “quieter” area of beamroom.
(Image courtesy Dr Andrew Alves)
Modern Tools for “Seeing” Atoms
Scanning Transmission Electron Microscope
Scanning Transmission Electron Microscope
Z-CONTRAST STEM IMAGING
ABERRATION CORRECTED STEM
Before Cs
correction
300 keV STEM AT ORNL HB603UX
with Nion aberration corrector
Modern Tools for “Seeing” Atoms
After Cs
correction
(Courtesy: Assoc. Prof Les Allen, School of Physics, Melb. Uni.)
Textbook Resources:
Fundamentals of Physics, Halliday, Resnick and Walker, John Wiley and
sons, New York,
Physics for Scientists and Engineers, 2nd Ed., Randall Knight, Pearson
source: http://cr4.globalspec.com/thread/59580/
What-is-magnetism
Sr
Ti
O
Structure of
SrTiO3
Melbourne Trams not allowed!
(Courtesy: Assoc. Prof Les Allen, School of Physics, Melb. Uni.)