M2
Magnetostatics
1
LECTURE 4
MAGNETOSTATICS
INTRODUCTION AND APPLICATIONS
(PART 1)
Outline
2
 Magnetism and magnets
 History
Hi t
off Magnets
M
t
 Types of Magnets
 Magnetic field
 Magnetic field line of forces
 Magnet applications
 Biot Savart’s law
 Gauss’s law
 Ampère’s law
1
Magnet song
3
Click on the image
http://www.youtube.com/watch?v=G-nkIECIBWM
Magnetism
4
 A physical phenomenon produced by the motion of electric charge,
resulting in attractive and repulsive forces between objects.
http://www.youtube.com/watch?v=XiHVe8U5PhU
2
What are magnets?
5
mag·net
ˈmagnət
noun
noun: magnet;
plural noun: magnets
a piece of iron (or an ore, alloy, or other material) that has its component atoms so
ordered that the material exhibits properties of magnetism, such as attracting
other iron-containing objects or aligning itself in an external magnetic field.
Iron
Nickel
http://periodictable.com/Samples/026.32/s13.JPG
http://images-of-elements.com/cobalt.jpg
Cobalt
http://www.periodictable.com/Samples/028.17/s7s.JPG
Polarization
6

Magnets are polarized.
Every
magnet has a north and a south.
N

Magnetic north and south poles are always together.
N

S
S
N
S
There are no magnetic monopoles.
3
History of Magnets
7
Click on the image
http://www.youtube.com/watch?v=u6v4J-CpKQE
Permanent Magnets
8
•
Once they have been magnetized they retain a certain degree of
magnetism.
Magnetite
http://www.periodictable.com/Samples/060.2/s9s.JPG
http://period8-2009.wikispaces.com/file/view/Magnetite.jpg/97048778/460x344/Magnetite.jpg
4
Shapes of Permanent Magnets
9
http://ed101.bu.edu/StudentDoc/Archives/ED101fa10/sjay0601/images/20060312083354!Bar_magnet.jpg
http://www.thomasnet.com/articles/image/electrical-power-generation/nib-magnet.JPG
http://www.heberger-image.fr/data/images/50198_aimant_different_modele.jpg
5
M2
Magnetostatics
1
LECTURE 4
MAGNETOSTATICS
INTRODUCTION AND APPLICATIONS
(PART 2)
Temporary magnets
2
•
•
Magnets that simply act like
permanent magnets when
they are within a strong
magnetic field.
Unlike permanent magnets
however, they loose their
magnetism when the field
disappears.
Paper clips
Iron nails
https://epay.hawaii.edu:8443/C24372test_ustores/web/images/store_9/paper_clip_large.jpg
http://www.commonnail.com/upfiles/common_nailswire_nailsiron_nails.jpg
1
Electromagnets
3
 Electromagnets are extremely strong magnets.
 Magnetic fields are induced by current (motion of electric charges)
 Electromagnets are widely used as components of other electrical
devices such as





Electrical motors
Maglev train
Headphones, stereo speakers, computer speakers
Phone ringers
Electron microscope, AFM, particle accelerator
I
http://upload.wikimedia.org/wikipedia/commons/4/41/Simple_electromagnet2.gif
Direct Current (DC) Motor
4
Magnet
Brush
Magnet
Electromagnet
Simple DC motor circuit
http://www.youtube.com/watch?v=Xi7o8cMPI0E
http://upload.wikimedia.org/wikipedia/commons/4/41/Simple_electromagnet2.gif
http://www.learningaboutelectronics.com/images/DC-motor-circuit.png
2
Speakers and Microphones
5
See how speakers work!!!
http://www.techhive.com/article/2000201/three-minute-tech-speakers.html
https://microphones.audiolinks.com/Microphones/micdiagram2922.jpg
http://www.youtube.com/watch?v=LKuHuyaRiHg
Electromagnet Ringer
6
3
Scanning Electron Microscope
7
Magnetic lens
http://4.bp.blogspot.com/3FrRlleSObY/TVvFCdSiNI/AAAAAAAAAEM/BRBw3hk45vQ/s200/Scanning+Electron+Microscope.jpg
http://nanolab.me.cmu.edu/projects/geckohair/images/CMU_NanoRobotics_Lab_Hierarchy_SEM.jpg
http://www.purdue.edu/rem/rs/graphics/sem2.gif
http://www.ammrf.org.au/myscope/images/tem/em-lens_function.png
ElectroMagnetic Suspension (EMS) Maglev Train
8
http://www.chinadiscovery.com/assets/images/shanghai/city-tour/shanghai-maglev-train.jpg
http://www.hk-phy.org/articles/maglev/german_e.gif
4
Magnetic field
9
•
Magnetic field is the space surrounding a magnet, in which
magnetic force is exerted.
attraction
repulsion
http://www.schoolphysics.co.uk/age11-14/Electricity%20and%20magnetism/Magnetism/text/Magnetic_fields/index.html
http://www.tutorvista.com/content/science/science-ii/magnetic-effects-electric-current/mapping-magnetic-lines.php
http://upload.wikimedia.org/wikipedia/commons/1/14/Magnetic_field_of_bar_magnets_repelling.png
Magnetic field
10
•
If a bar magnet is placed in
the magnetic field, it will
experience magnetic forces.
However, the field will
continue to exist even if the
magnet is removed.
S
N
http://www.superconductors.solidchem.net/sites/default/files/users/user1/MagnetSchoolFSU-Electromagnet.png
5
Magnetic Lines of Force
11
•
•
A magnetic field is described by drawing the magnetic lines of force.
A magnetic line of force is the path traced by a North magnetic pole
free to move under the influence of a magnetic field.
6
M2
Magnetostatics
1
LECTURE 4
MAGNETOSTATICS
INTRODUCTION AND APPLICATIONS
(PART 3)
Properties of Magnetic Lines of Force
2
•
•
•
•
Lines of force are closed and
continuous curves.
Outside the magnet, the lines
of force are directed from the
north pole toward the south
pole of the magnet, whereas
within the magnet the
magnetic lines are directed
from the south pole towards
the north pole.
pole
Lines of force repel each
other.
Lines of force never intersect.
http://www.youtube.com/watch?v=zbTrHWW3xvU
1
How is magnetic field created?
3
Oersted’s experiment
Oersted
Oersted’ss
experiment shows that current produces magnetic
fields that loop around the conductor.
Click on the image
http://www.youtube.com/watch?v=-w-1-4Xnjuw
How is a magnetic field created?
4
 Magnetic fields are produced by the motion of electrical charges.
 Therefore, the current can produce the magnetic field.
http://demonstrations.wolfram.com/CreationOfAMagneticFieldByAnElectricCurrent/
2
Magnetic field intensity in other
configurations
5
SOLENOID
CLICK here!
http://www.quantumdiaries.org/wp-content/uploads/2011/05/Solenoid.jpeg
TOROID
CLICK here!
http://www.wb5rvz.com/sdr/common/images/toroid_coil_22_turns.gif
Earth’s Magnetic Field
6
• The Earth's magnetic field is similar
to that of a bar magnet tilted 11
degrees from the spin axis of the
Earth.
• The circulating electric currents in
the Earth's molten metallic core are the
origin of the magnetic field which gives a
field similar to that of the earth.
• The magnetic field magnitude
measured at the surface of the Earth is
about half a Gauss and dips toward the
Earth in the northern hemisphere.
http://www.physics.sjsu.edu/becker/physics51/mag_field.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magearth.html
3
Earth’s Magnetic Field
7
•
Earth’s magnetic field is a great shield to cosmic rays.
Click on the image
http://www.youtube.com/watch?v=URN-XyZD2vQ
Can the Earth’s Magnetic Field Flip?
8
•
What happens if the earth’s magnetic field flips ?
4
Which type of field is present near a moving
electric charge?
9
a)
b)
c)
d)
Both an electric field and a magnetic field
Neither an electric field nor a magnetic field
An electric field only
A magnetic field only
http://www.youtube.com/watch?v=uj0DFDfQajw
5
M2
Magnetostatics
1
LECTURE 4
MAGNETOSTATICS
BIO SAVART’S LAW
Magnetic Field Intensity Calculation
2
H
Vector quantity
Unit: Ampere/m
1
Biot Savart’s Law
3
http://iesmonre.educa.aragon.es/alumnos0506/electricidad/biotsavart/biografia.htm
Biot Savart’s Law
4
Biot-Savart law states that
“If a wire carries a steady current I, the magnetic field dH at
some point P associated with an element of conductor length
dl has the following properties:
• The vector dH is perpendicular to both dl (the direction
of the current I) and to the unit vector r directed from
the element dl to the point P.”
2
Biot Savart’s Law
5

H = magnetic field intensity (A/m)
I = electric current (A)

dl = line segment vector (m)

r = distance vector from a current line to
point P (m)
r = distance from a current line to point P
(m)
dH
aˆ r = unit vector with the direction from a
current line to point P
AP Physics C Montwood High School R. Casao
Mathematical Form of Biot Savart’s Law
6
Magnetic field from the current segment dl is

 
 Idl  a r Idl  r
dH 

4 r 2
4 r 3
A/m
The integration is required over the length l.
 

Idl  r
H 
4 r 3
A/m
3
Recalling Coulomb’s law: Line of charge (1)
Consider a charged wire, the test charge q0 is placed to
measure the electric field at that position using Coulomb’s
 
law.

E E
En
2
+ q0
1
+
rn
r1
r2

E
q1
+ +
+ q1 + q2
aˆ 
2 1
4 0 r1
q2
+
+ qn
aˆ  ... 
2 2
4 0 r2
qn
4 r
2
0n
aˆ n  ...
For a continuous point charges, it is impossible to find the
superpositioned electric field of a charged wire!
Recalling Coulomb’s law:
 Line of charge (2)
Consider the electric field dE from each charge
element dq along a charged wire of length l using

Coulomb’s law.

dq
dE
dE 
+
+ q0
r
+
dq
l
4 0 r 2
aˆ r

dq
E
aˆ
2 r
4 0 r
l

1
dqq
aˆ r
4 0 l r 2
The problem can be solved using vector calculus.
4
Solving the Magnetic Field for Line of Current
by Bio Savart’s Law (Coulomb’s Law Analogy)
9
z
Assumption: current elements are discrete.
I
P
r1
Using Superposition to Obtain the Total Magnetic
Field.
10
z
Calculation of the magnetic field from each element
I
r2
rn
……….
r1
P

 
 r1 Idl1  r1
 Idl1  a
dH 1 

4 r12
4 r13

Idl 2  r 2
dH 2 
4 r23
 

Idl n  r n
dH n 
4 rn 3
5
For Continuous Line of Current, It is Impossible to
Find the Magnetic Field by Superposition.
11
The integration is required over the length l.
 

Idl  r
H 
4 r 3
A/m
Step by Step:
Magnetic Field in a Current-Conducting wire
12

z
Find Idl

Idl  Idza
Id ˆ z
I
y

Find r
dl
r

r  yaˆ y  zaˆ z
http://www.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Magnetism/Images/biot.jpg
6
Step by Step:
Magnetic Field in a Current-Conducting wire
13
z
 
Idl  r  Idzaˆ z  ( yaˆ y  zaˆ z )
I
y
P
 
Idl  r  Iydz (aˆ x )
dl
http://www.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Magnetism/Images/biot.jpg
Step by Step:
Magnetic Field in a Current-Conducting wire
14
z
 3  2 2 3
r  r  (z  y )


3
I
dH1
x
P
dl
y
 (z2  y2 )3/2
 

Idl  r Iydz (aˆ x )
dH 1 
 2
3
4 r
( z  y 2 )3/2
http://www.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Magnetism/Images/biot.jpg
7
Step by Step:
Magnetic Field in a Current-Conducting wire
15


H 1   dH 1
From

Iydz (aˆ x )
( z 2  y 2 )3/2

 Iy 
dz
(aˆ x )
2
2 3/2
(z  y )
Step by Step:
Magnetic Field in a Current-Conducting wire
16
Using the formula from Table of Integral

yields
a
dx
2
x
2

3

2

x
a  a  x2
2
2

I
(aˆ x )
H1 
2 y

1
2
A/m
/
8
If we calculate for H field at the same radial distance  from
the current wire, we will obtain the same magnitude of the
magnetic field as
z
dH
dH
I
H
dH
2
A/m
dH
y
x

dH
I
dH
x
17
Right Hand Rule
18
The right hand rule can be used to
determine the direction of the magnetic
field around the current carrying
conductor:
Thumb of the right hand in the
direction of the current.
Fingers of the right hand curl
around the wire in the direction of
the magnetic field at that point.
H
http://scienceblogs.com/startswithabang/files/2009/04/Right_hand_rule.png
9
Magnetic Field in a Current-Conducting wire
19
CLICK
http://www.walter-fendt.de/ph14e/mfwire.htm
Summary of the Magnetic Field of the Conducting Wire
20
• The magnetic field lines are concentric circles that surround the wire in a
plane perpendicular to the wire.
• The magnitude of the magnetic field H is proportional to the current and
decreases as the distance from the wire increases.
H
Watch this cool animation!
AP Physics C Montwood High School , R. Casao
10
1
 In our living world (macroscopic world), magnetism
arises from magnets (hard and soft magnetic
materials), electromagnets, and current flow.
Flow of current in a coil
causes magnetism
Magnet causes
magnetism
2
 Technically speaking, we say that the source of
magnetism
g
is a magnetic
g
dipole
p
moment.
N
S
1
3
• At atomic and molecular levels (microscopic world),
electrons
: move in orbits around a nucleus similar to the
earth moves in an orbit around the sun,
: rotates (spin) around their own axes similar to
the earth rotates around its own axis.
• Movement of electrons in orbits and electron spin
are equivalent
q i l t to
t charge
h
movementt and
d is
i the
th source off
magnetism or dipole moments. We can call them orbital
dipole moment and spin dipole moment, respectively.
4
• In fact, the origin of all magnetism in magnetic
materials are due to movement of electrons in orbits and
electron spin.
Magnetic dipole moment
due to electron moving
in orbit around nucleus
Magnetic dipole moment
due to electron spinning
around its own axis
• Net dipole moment of an atom is a vector sum of all
orbital and spin dipole moments through their
interaction. Imagine complexity of interactions of 26
orbital moments and 26 spin moment in one iron atom.
2
5
• When Fe atoms (and other magnetic atoms such as
Ni Co) form solids,
Ni,
solids net moments of atoms further
interact. This will cause net moments to point, to align,
in the same direction within a small region called a
magnetic domain.
• Each domain will have a
net dipole
p
moment, call
magnetization, in one direction
only. Sizes of magnetic domains
are few tens of microns.
• Different domains have
different magnetization.
6
• A piece of magnetic materials
(such as magnets) have millions
off domains.
d
i
L ft in
Left
i nature,
t
th
they
show no magnetism as net
moments of different domains
point in different directions. We
can see domains with Kerr
Microscopy technique.
3
7
• We can force moments in different domains to align
in the same direction by applying external magnetic fields
from permanent magnets or electromagnets.
• Apply magnetic fields will exert force on moments in
domains so that they are parallel applied field. Under such
Condition, we say that materials
- show net dipole moment,
- exhibit magnetism,
magnetism
- become magnetized.
8
4