Download mag01

PHYS2012
mag01.doc
MAGNETISM AND ELECTRIC CARS
Powerful magnets are essential components in motors and generators for the use in
electric and hybrid-electric cars. Some electric motors and generators rely upon a
combination of a permanent and an electromagnet. An electric motor converts electrical
energy into mechanical energy by the torque acting on a conductor carrying an electric
current in a magnetic field. A generator converts mechanical into electrical energy by
moving a conductor through a magnetic field.
What is a magnet and what is meant by a magnetic field?
The goal of this part of the course on the Magnetic Properties of Materials is to gain a
knowledge and understanding of permanent and electromagnets and to appreciate the role
of magnetism in our technological world. We will consider magnetism from microscopic
(atomic) and macroscopic points of view.
A magnet is a material or object that produces a magnetic field. This magnetic field is
invisible but is responsible for the most notable property of a magnet: a force that pulls
on other ferromagnetic materials like iron and attracts or repels other magnets. A
permanent magnet is an object made from a material that is magnetized and creates its
own persistent magnetic field. Materials that can be magnetized, which are also the ones
that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic). These
include iron, nickel, cobalt, some alloys of rare earth metals, and some naturally
occurring minerals such as lodestone. Although ferromagnetic (and ferrimagnetic)
materials are the only ones attracted to a magnet strongly enough to be commonly
considered magnetic, all other substances respond weakly to a magnetic field, by one of
several other types of magnetism.
Ferromagnetic materials can be divided into magnetically "soft" materials like annealed
iron which can be magnetized but don't tend to stay magnetized, and magnetically "hard"
materials, which do. Permanent magnets are made from "hard" ferromagnetic materials
which are subjected to special processing in a powerful magnetic field during
manufacture, to align their internal microcrystalline structure, making them very hard to
demagnetize.
An electromagnet is made from a coil of wire which acts as a magnet when an electric
current passes through it, but stops being a magnet when the current stops. An
electromagnet in its simplest form, is a wire that has been coiled into one or more loops,
known as a solenoid. The magnetic field that is generated is concentrated near (and
especially inside) the coil, and its field lines are very similar to those for a magnet. If the
coil of wire is wrapped around a material with no special magnetic properties it will tend
to generate a very weak field. However, if it is wrapped around a soft ferromagnetic
material then the net field produced can result in a several hundred to thousand fold
increase of field strength.
mag01.doc
May 2, 2017
1
Magnetic field surrounding a bar magnet
Magnetic field lines of a solenoid – magnetic
field pattern is similar to that of a bar magnet
The magnetic field (usually denoted B ) is a vector field and is more precisely called the
magnetic induction, magnetic flux density or B-field. The magnetic field vector at a given
point in space is specified by two properties:
1. Its direction, which is along the orientation of a compass needle.
2. Its magnitude (also called strength), which is proportional to how strongly the
compass needle orients along that direction.
In SI units, the strength of the magnetic field B is given in teslas [T].
Common uses of magnets
 Magnetic recording media: VHS tapes and audio cassettes contain a reel of
magnetic tape. The information that makes up the video and sound is encoded on the
magnetic coating on the tape. Computers, floppy and hard disks record data on a thin
magnetic coating.
 Credit, debit, and ATM cards: have a magnetic strip on one side.
 Common televisions and computer monitors: TV and computer screens containing
a cathode ray tube employ an electromagnet to guide electrons to the screen.
 Speakers and microphones: Most speakers employ a permanent magnet and a
current-carrying coil to convert electric energy (the signal) into mechanical energy
(movement which creates the sound). The coil is wrapped around a bobbin attached to
the speaker cone, and carries the signal as changing current which interacts with the
field of the permanent magnet. The voice coil feels a magnetic force and in response
moves the cone and changes the pressure the neighboring air, thus generating sound.
Dynamic microphones employ the same concept, but in reverse. A microphone has a
diaphragm or membrane attached to a coil of wire. The coil rests inside a specially
shaped magnet. When sound vibrates the membrane, the coil is vibrated as well. As
mag01.doc
May 2, 2017
2









the coil moves through the magnetic field, a voltage is induced across the coil. This
voltage drives a current in the wire that is characteristic of the original sound.
Medicine: Hospitals use Magnetic Resonance Imaging (MRI) to spot problems in a
patient's organs without invasive surgery.
Transformers: are devices that transfer electric energy between two windings of
wire that are electrically isolated but are coupled magnetically.
Compasses: is a magnetized pointer free to align itself with a magnetic field, most
commonly Earth's magnetic field.
Art: Vinyl magnet sheets may be attached to paintings, photographs, and other
ornamental articles, allowing them to be attached to refrigerators and other metal
surfaces.
Toys
Magnets can pick up magnetic items (iron nails, staples, tacks, paper clips) that are
either too small, too hard to reach, or too thin for fingers to hold. Some screwdrivers
are magnetized for this purpose. Magnets can be used in scrap and salvage operations
to separate magnetic metals (iron, steel, and nickel) from non-magnetic metals
(aluminium, non-ferrous alloys, etc.). The same idea can be used in the so-called
magnet test, in which an auto body is inspected with a magnet to detect areas repaired
using fiberglass or plastic putty.
Magnetic levitation transport, or maglev, is a form of transportation that suspends,
guides and propels trains through electromagnetic force. The maximum recorded
speed of a maglev train is 581 km.h-1.
Health: human tissues have a very low level of susceptibility to static magnetic
fields, there is little mainstream scientific evidence showing a health hazard
associated with exposure to static fields. Dynamic magnetic fields may be a different
issue however; correlations between electromagnetic radiation and cancer rates have
been postulated due to demographic correlations. If a ferromagnetic foreign body is
present in human tissue, an external magnetic field interacting with it can pose a
serious safety risk. A different type of indirect magnetic health risk exists involving
pacemakers. If a pacemaker has been embedded in a patient's chest (usually for the
purpose of monitoring and regulating the heart for steady electrically induced beats),
care should be taken to keep it away from magnetic fields or metal detectors at
airports. It is for this reason that a patient with the device installed cannot be tested
with the use of an MRI, which is a magnetic imaging device. Children sometimes
swallow small magnets from toys; and this can be hazardous if two or more magnets
are swallowed, as the magnets can pinch or puncture internal tissues; one death has
been reported.
Motors and generators
mag01.doc
May 2, 2017
3
Types of permanent magnets
Magnetic metallic elements - when the electron spins interact with each other in such a
way that the spins align spontaneously, the materials are called ferromagnetic. Because of
the way their regular crystalline atomic structure causes their spins to interact, some
metals are ferromagnetic when found in their natural states, as ores. These include iron
ore (magnetite or lodestone), cobalt and nickel, as well the rare earth metals gadolinium
and dysprosium (when at a very low temperature).
Ceramic or ferrite magnets are made of a sintered composite of powdered iron oxide
and barium/strontium carbonate ceramic. Given the low cost of the materials and
manufacturing methods, inexpensive magnets (or non-magnetized ferromagnetic cores,
for use in electronic component such as radio antennas, for example) of various shapes
can be easily mass-produced. The resulting magnets are non-corroding, but brittle and
must be treated like other ceramics.
Alnico magnets are made by casting or sintering a combination of aluminium, nickel and
cobalt with iron and small amounts of other elements added to enhance the properties of
the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers
higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist
corrosion and have physical properties more forgiving than ferrite, but not quite as
desirable as a metal.
Ticonal magnets are an alloy of titanium, cobalt, nickel, and aluminium, with iron and
small amounts of other elements, often used in loudspeakers.
Injection molded magnets are a composite of various types of resin and magnetic
powders, allowing parts of complex shapes to be manufactured by injection molding. The
physical and magnetic properties of the product depend on the raw materials, but are
generally lower in magnetic strength and resemble plastics in their physical properties.
Flexible magnets are similar to injection molded magnets, using a flexible resin or binder
such as vinyl, and produced in flat strips, shapes or sheets. These magnets are lower in
magnetic strength but can be very flexible, depending on the binder used. Flexible
magnets can be used in industrial printers.
Rare earth magnets (lanthanoid) elements have a partially occupied f electron shell
(which can accommodate up to 14 electrons.) The spin of these electrons can be aligned,
resulting in very strong magnetic fields, and therefore these elements are used in compact
high-strength magnets where their higher price is not a concern. The most common types
of rare earth magnets are samarium-cobalt and neodymium-iron-boron (NIB) magnets.
One of the most widely used of the group of elements known as lanthanides or rare earth
elements, is neodymium. Neodymium magnets have a much higher magnetic strength
than other permanent magnets. It is the largest constituent of a new type of high-strength
magnets that are used to increase the power and reduce the size and weight of electric
motors. This makes them indispensible for the new generation of hybrid and electric cars,
the miniaturization of hard disk drives, and also the construction of wind turbines, which
also depend on strong magnetic fields to generate electricity. Toyota Prius car requires
one kilogram of neodymium.
mag01.doc
May 2, 2017
4
Magnetic materials
The term magnet is typically reserved for objects that produce their own persistent
magnetic field even in the absence of an applied magnetic field. Only certain classes of
materials can do this. Most materials, however, produce a magnetic field in response to
an applied magnetic field; a phenomenon known as magnetism. There are several types
of magnetism, and all materials exhibit at least one of them. The overall magnetic
behavior of a material can vary widely, depending on the structure of the material, and
particularly on its electron configuration. Several forms of magnetic behavior have been
observed in different materials, including:
Ferromagnetic and ferrimagnetic materials are the ones normally thought of as
magnetic; they are attracted to a magnet strongly enough that the attraction can be felt.
These materials are the only ones that can retain magnetization and become magnets.
Ferrimagnetic materials, which include ferrites and the oldest magnetic materials
magnetite and lodestone, are similar to but weaker than ferromagnetics. The difference
between ferro- and ferrimagnetic materials is related to their microscopic structure.
Paramagnetic substances such as platinum, aluminium, and oxygen are weakly attracted
to a magnet. This effect is hundreds of thousands of times weaker than ferromagnetic
materials attraction, so it can only be detected by using sensitive instruments, or using
extremely strong magnets.
Diamagnetic means repelled by both poles - such as carbon, copper, water, and plastic
which are weakly repelled by a magnet. All substances not possessing one of the other
types of magnetism are diamagnetic; this includes most substances. Although force on a
diamagnetic object from an ordinary magnet is far too weak to be felt, using extremely
strong superconducting magnets diamagnetic objects such as pieces of lead and even
mice can be levitated so they float in mid-air. Superconductors repel magnetic fields from
their interior and are strongly diamagnetic.
M780
mag01.doc
May 2, 2017
5
MICROSCOPIC ORIGIN OF MAGNETISM
Every electron, on account of its spin, is a small magnet. In most materials, the countless
electrons have randomly oriented spins, leaving no magnetic effect on average. However,
in a bar magnet many of the electron spins are aligned in the same direction, so they act
cooperatively, creating a net magnetic field. In addition to the electron's intrinsic
magnetic field, there is sometimes an additional magnetic field that results from the
electron's orbital motion around the nucleus. This effect is analogous to how a currentcarrying loop of wire generates a magnetic field. Ordinarily, the motion of the electrons is
such that there is no average field from the material, but in certain conditions, the motion
can line up so as to produce a measurable total field.
Orbital magnetic moment
An electron moving in a circular orbit around a nucleus produces an average current i
along its orbit.
q e
i

t T
where T is the orbital period of the electron.
Suppose the electron is moving with a velocity v in a circular orbit with radius R. (This is
a classical picture which is useful but not correct). The orbiting electron possesses an
angular moment L and is related to the period T by
2 R 2 me
2 R
L  me v R
v
T
T
L
The circular current loop is a very important idea because it leads to the concept of the
magnetic dipole and its magnetic dipole moment pm .
B
right hand
screw rule
magnetic dipole moment
pm
pm  i A
At a point along the axis
i
current loop in xy-plane
Bz 
z >> a
0
iA
2 z 3
As a consequence we can associate a magnetic dipole moment pm with the orbiting
electron and the magnetic dipole moment gives a magnetic field surrounding it.
mag01.doc
May 2, 2017
6
 Le 
eL
e
2
pm  I A     R 2   
  R  
2
2 me
T 
 2 R me 
pm  
eL
2 me
Magnetic dipole moment and angular momentum point in opposite directions. Since this
magnetic dipole moment is associated with the orbital motion of the electron around the
nucleus it is called the orbital magnetic moment.
The state of an electron in an atom is described by a set of four quantum numbers:
n = 1, 2, 3, ….
principle quantum number (energy – shells)
l = 0, 1, …, (n-1)
angular momentum quantum number (subshells)
ml = 0, 1, …, l
magnetic quantum number (orientation of subshells)
ms = 1/2
spin quantum number
The angular momentum of the electron is quantized. Assume that there exists an external
magnetic field Bz directed in the +Z direction. Then the components of the angular
momentum in the Z direction can only have values given by
h
Lz  ml

2
and the orbital magnetic moment aligned with the magnetic field can only have values
eL
e
pm   z  
ml  uB ml
2 me
2 me
e
 9.27 1024 A.m 2 is called the Bohr magneton. The orbital magnetic
where uB 
2 me
moments of atoms are in the order of a Bohr magneton.
When ever a charged particle has angular momentum, the particle will contribute to the
permanent magnetic dipole moment. The total orbital magnetic moment of an atom is
equal to a vector sum of the orbital magnetic moments of each electron. For atoms with
completely filled shells  zero orbital magnetic moment eg
n = 2 l = 1 ml = -1, 0, +1
all states occupied  sum of all components of angular momentum cancel.
Transition elements
Incomplete filled inner shells  free atoms do have resultant orbital magnetic
moments. Solid iron group – magnetic dipoles can not align  no major
contribution to magnetic properties.
Fe Z = 26
1s2 2s22p6 3s23p63d6 4s2
3d subshell incomplete
Orbital angular magnetic moment is not a major contribution to the magnetic properties
of materials.
mag01.doc
May 2, 2017
7
Spin Magnetic Moment
Another contribution to the magnetic moment is due to the rotational motion of the
electron. Classically we can regard an electron as a small ball of negative charge spinning
around its axis, hence it possesses spin angular momentum S . Assume that there exists
an external magnetic field Bz directed in the +Z direction. Then the components of the
spin angular momentum in the Z direction can only have values given by
1
S z  ms
ms  
2
The two states are often referred to as spin up and spin down  states. The spin angular
momentum produces a magnetic dipole moment
eS
pm  
me
and the spin magnetic moment aligned with the magnetic field can only have values
e
e
pm   ms  2uB ms
uB 
me
2 me
pm   uB
Fe Z = 26
1s2 2s22p6 3s23p63d6 4s2
3d subshell incomplete
3d subshell (6 electrons)
    
Iron atom spin angular momentum +4
Metallic iron angular momentum +2.2  magnetic properties of iron.
The total magnetic moment of an atom is equal to the vector sum of the orbital magnetic
moments and the spin magnetic moments of all its electrons. The contribution of the
nuclear magnetic moment is small and often can be neglected. Each atom acts like a
magnetic dipole and produces a small, but measurable magnetic field.
Paramagnetism - even though each atom in a material can have a magnetic moment, the
direction of each dipole is randomly oriented and their magnetic fields average to zero. If
the material is immersed in an external magnetic field, the dipoles will tend to align
themselves with the field in order to minimize the torque exerted on them by the external
magnetic field (lowest energy). The atoms in the material will produce an extra magnetic
field in its interior that has the same direction as the external magnetic field. This increase
in strength of the magnetic field can be quantified in terms of the relative permeability of
the material B = r Bfree.
Ferromagnetism - the alignment of the spins of some of the electrons in a ferromagnetic
material will increase the magnetic field in this material in much the same way as the
alignment of the orbital magnetic dipole moments of atoms increases the field strength in
a paramagnetic material. In a ferromagnetic material the degree of alignment of the
electron spins between neighboring atoms is high as a result of a special force that tends
to lock the spins of these electrons in a parallel direction. This force is so strong that the
spins remain aligned even when the external magnetic field is removed. Materials with
mag01.doc
May 2, 2017
8
such properties are called permanent magnets. The force that is responsible for the
alignment of the electron spins occurs in only five elements:
Iron
Nickel
Cobalt
Dysprosium
Gadolinium
Although ferromagnetic materials will remain magnetized after the external magnetic
field has been removed, they can also be found in non-magnetized states. On a small
scale (domains with sizes of less than 0.1 - 5 mm) all spins will be perfectly aligned, on a
large scale the domains are oriented randomly, and the net magnetic field is equal to zero.
However, if the material is immersed in an external magnetic field, all dipoles will tend
to align along the external field lines, and the strong spin-spin force will keep the dipoles
aligned even after the external magnetic field has been removed. The increase of the
magnetic field in a ferromagnet can be very large. For iron, the increase in field strength
can be as large as 5000. The degree of alignment of the spins in a ferromagnetic
material after the external magnetic field has been removed depends on the temperature.
An increase in the temperature of the material will increase the chance of random
rearrangement of the magnetic dipoles. Above a certain temperature, called the Curie
temperature TC, the magnetism of the ferromagnet disappears completely and acts like a
paramagnetic material.
Ferrimagnetic material – permanent dipoles with anti-parallel orientation of unequal
amounts of spin


Important material because electrical conductivity like a semiconductor or insulator.
DC resistivity many orders of magnitude greater than iron  eddy current problem of
preventing penetration of magnetic flux into material much less severe in ferrites than
iron. Ferrites used in transformer cores up to microwave frequencies.
Structure very important for the magnetic properties of ferrites
X Fe23+ O4where X  Fe2+
M314
mag01.doc
M736
Co2+ Mn2+ Zn2+ Cd2+ Mg2+
M978
M988
May 2, 2017
9
MEASURING MAGNEITC FIELDS – HALL EFFECT
The Hall Effect is the production of a voltage difference (Hall voltage) across an
electrical conductor, transverse to an electric current in the conductor and a magnetic
field perpendicular to the current. Edwin Hall discovered this effect in 1879. A Hall
probe can be used to measure the magnetic field B, number density n for the charge
carriers and to determine the sign of charge carriers (+ or -)
Y
thickness t
area A = w t
width w
X
I
current in
X direction
Z
B
magnetic field in Z direction
Schematic diagram of a Hall Probe
As the charge carriers q move through the Hall Probe, they will experience a force due to
the magnetic field B. The charges will be deflected down if they are positive (-Y
direction) or deflected up if they are negative (+Y direction). Therefore, a Hall voltage VH
will be established across the probe and the polarity of the Hall voltage will give the sign
of the charge carriers.
charge carriers electrons (-)
eg wire, N-type semiconductor
VH
w
VH   EH w
EH  
+
-
+
-
+
-
+
-
VH
+
EH
+
out of page
-
+
_
EH
-
.
B Z direction
+
-
I
+
-
X
+
-
+
VH
-
width
w
Y
charge carriers positive (+)
eg holes in P-type semiconductor
VH
w
VH   EH w
EH  
N.B. t is thickness of the material in a direction parallel to B and w is the width in a
direction perpendicular to B .
mag01.doc
May 2, 2017
10
The Hall voltage gives rise to an electric field EH in the Y direction so that the electrical
force FE on the charge carriers is in the opposite direction to the magnetic force FM. A
steady state situation will be reached when FE = FM.
Magnetic force
FM  q v B
Electric force
FE  q EH
Steady State
FM = FE
EH = v B
B
EH
v
Current
I
q
 n q vd A  n q vd wt
t
Drift velocity
vd 
Electric field
EH 
Hall voltage
VH  E H w 
Magnetic field
B
n q tVH
I
Number density charge carriers
n
IB
q tVH
M102
M174
M295
M102
M174
M295
I
n q wt
IB
n q wt
M314
IB
n qt
M736
M780
M978
M988
Some of the notes were sourced from
http://en.wikipedia.org/wiki/Magnet
mag01.doc
May 2, 2017
11