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awfulhihatUrban and Civil

Nov 15, 2013 (3 years and 10 months ago)

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Lecture 24

Magnetic materials.

Magnetic field by a dipole

B

field lines for a current loop

Somehow, it must be the same thing…

B

field lines for a magnet

DEMO:
B field lines of
a magnet

Back to current loops

For a current loop of area
A

and current
I
:

IA


No net force on a current loop in a uniform magnetic field, but how
about a non
-
uniform magnetic field?

z

R

I

A
Magnetic moments

anti
-
parallel


repulsion

Magnetic moments

parallel


attraction

Dipole
-
dipole interaction

=


=

Parallel currents:
attraction

N
S

N
S

N
-
S: attraction

=

Antiparallel
currents: repulsion

N
S

S

N

S
-
S (or N
-
N): repulsion

N
S

=

DEMO:
Magnets

Somehow, loops and magnets must be the same thing…

Magnetism in materials

Orbits of
electrons
about nuclei

2. Intrinsic “spin” of electrons (most important effect)

1.
Currents at atomic level within bulk matter

In general, these atomic magnetic dipoles point in random
direction, so material does not produce a net magnetic field.

Where are the currents in magnets?!?

Magnetization

Let be the total magnetic moment of the material in a
sample with volume
V
.


total


total
M
V
Magnetization
of the sample




B
Compare to for a current loop!


 
0 0
B B M
Total magnetic field in the sample

External (applied)
magnetic field

Part due to do magnetic
properties of the sample

Magnetic permeability and susceptibility

0
and
B M
In the simplest cases, are either parallel or antiparallel, so
we can write:


  
0 0 0
M
B B M KB


 

  
0 0
0 0
1
M
B B B
M K
K
M

Magnetic permeability


0
M
B KB

 
1 Magnetic susceptibility
M M
K



0
0
M
B
M
Note: Both quantities are dimensionless.

Magnetic materials


Materials can be classified by how they respond to an applied
magnetic field
B
0
.



Paramagnetic

(
χ
M

> 0)


Diamagnetic

(
χ
M

< 0)


Ferromagnetic (it’s complicated…)

Paramagnetic materials

Examples: aluminum, tungsten, oxygen,…



Atomic magnetic dipoles (~tiny magnets) tend to
line up with the field,
increasing

it








χ
M

> 0 and
K
M

> 1



Thermal motion randomizes their directions, so only a small effect
persists:
B
ind

~ B
0
×

10
−5

(
i.e.,
χ
M

~ 10
−5
, K
M
~ 1
)



Paramagnetic materials are very slightly attracted to the source of the
external magnetic field.







 


0 0
0
0
0
M
M
B B M
B
M
B KB
B
0


B
0

= 0

Diamagnetic materials

Examples: gold, copper, water,…



Atomic dipole moments are zero unless an external
B
0

is applied



In the presence of external

B
0
, atomic magnetic dipoles are induced,
they
oppose the applied magnetic field,
reducing

it








χ
M

< 0 and 0 >
K
M

> 1



Again, this is usually very weak;
B
ind

~ −
B
0
×

10
−5

(
i.e.,
χ
M

~
-
10
−5
,
K
M
~ 1
)



Diamagnetic materials are repelled by the source of the external
magnetic field






 


0 0
0
0
0
M
M
B B M
B
M
B KB
B
0

B
0

= 0



0
Levitating graphite:

http://www.youtube.com/watch?v=lnjXleg
-
68A

Levitating of frog (water!):

http://www.youtube.com/watch?v=A1vyB
-
O5i6E

Repulsion


magnetic
levitation!

ACT: Superconductors

Superconductors are materials with zero electric resistance. Inside
superconductors, the magnetic field is always zero (even when there
is an external applied magnetic field). This means superconductors
are:

A.
Perfect diamagnetic materials


B. Perfect paramagnetic materials



Perfect diamagnetism: superconductors


0
B

 
0
0
B
M
χ
M

=

1

K
M

= 0

The big dipole moment comes from
macroscopic

current loops.

(Resistance is zero, currents are “free”!)

B
0

B
0

= 0


I




 


0 0
0
0
0
M
M
B B M
B
M
B KB
Levitating magnet over superconducting ceramic:

http://www.youtube.com/watch?v=nWTSzBWEsms

Ferromagnetic materials

Examples: iron, cobalt, nickel,…



Somewhat like paramagnetic, dipoles prefer to line up with the
applied field.



Big difference: there is a complicated
collective effect
due to
strong interactions between neighboring dipoles (
domains
) that
overcomes thermal disorder


they tend to all line up the same
way.



Very strong enhancement
.

B
ind

~ B
app
×

10
5



Strong attraction.


DEMO:
Electromagnet
with nails

Ferromagnetic domains


Even when
B
ext

= 0, the dipoles
tend to strongly align over small
patches.


DEMO:
Domains


When
B
ext

is applied, the domains
align to produce a large net
magnetization.

Soft ferromagnets

The domains re
-
randomize when the field is removed.

B
0

M

Hard ferromagnets


The domains persist when
the field is removed.

B
0

M


Domains may be aligned in a
different direction by applying a
new field



Domains may be re
-
randomized by
sudden physical shock



If the temperature is raised above
the “Curie point” (770
°
C

for iron),
the domains will also randomize


paramagnet

“Permanent”
magnet!

B
0

= 0 but
M

≠ 0

Hysteresis loop

ACT: Video tape

Which kind of material would you use in a video tape?

A.
Diamagnetic

B.
Paramagnetic

C.
Soft ferromagnetic

D.
Hard ferromagnetic

Diamagnetism and paramagnetism are far too weak to be used for a
video tape. Since we want the information to remain on the tape
after

recording it, we need a “hard” ferromagnet. These are the
key to the information age

cassette tapes, hard drives, credit
card strips,…

Fridge magnets

How does a magnet attract screws, paper clips, refrigerators, etc?

The materials are all “soft” ferromagnets. The external field
temporarily aligns the domains so there is a net dipole, which
is then attracted to the bar magnet.


-

The effect vanishes with no applied
B

field


-

It does
not

matter which pole is used.

Compare to: Electric polarization
of materials, balloon that sticks
to the wall

N

S