Magnetic properties of materials- I
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Transcript Magnetic properties of materials- I
Magnetic
properties of
materials- I
Magnetic properties
of materials- I
Magnetic dipoles
Field of a magnetic dipole
Force on a dipole in a non uniform
field
Induced magnetic dipole moment
Circular current loop
B
p
dB
B
r
z
0 I
2
R
R
2
2
z
2 3/ 2
Circular current loop
B
0 I
2
R
R
2
z
If z >>R
B
0 I R
2 z
2
2
3
0 I R
B
3
2 z
2
2 3/ 2
0
B
3
2z
Where is =
2
R
I
Known as Magnetic dipole moment
• and B are in the same direction.
• B is produced by .
• In general, = I A,
true for any shape of
the loop.
• A is a vector area,
with direction assign
by right hand rule.
Magnetic dipole in an external
Magnetic field
Magnetic
dipole
experiences a
torque
Torque of a current loop
B B0 zˆ
z
n
h
y
e
x
g
f
Torque on a current loop
z
B B0 zˆ
n
h
y
e
g
a
b
x
f
Plane of the loop makes
angle with the field
nˆ
B
z
e
b
y
f
Fef IbB sin(90 ) ( xˆ)
nˆ
B
z
h
b
y
g
Fgh IbB sin(90 ) (xˆ)
z
n
Forces on a current loop
h
e
y
g
b
x
a
f
Ffg IaB
Fhe IaB
( y direction)
( y direction)
y
Forces on a current loop
Fef IaB sin(90 )
Fgh IaB sin(90 )
( x direction)
( x direction)
Ffg IaB
Fhe IaB
( y direction)
( y direction)
Contribute to torque
r F
nˆ
b
R IaB sin xˆ
2
b
L IaB sin xˆ
2
z
Fhe
e
y
f
Ffg
Torque on a current loop
IabBsin xˆ
IABsin xˆ
NIA (nˆ B)
Torque of a magnetic
dipole
IA nˆ B
B
Torque tends to rotate
so that it lines up
with B.
Potential energy for the
dipole
• B makes an angle with the dipole
U d
U B
U has smallest value when and B are
parallel
- B
Largest when anti-parallel B
Find the magnetic dipole moment
of the circuit.
iA
i
a b
2
2
2
Find the magnetic
dipole moment of the
loop. All sides have
equal length and it
carries a current I.
z
a
a y
x
a
Ia yˆ Ia zˆ
2
2
Direction is along
the line y = z.
Important to note
• In general, potential energy (PE) can not
be defined for a Magnetic field alone.
• Since torque on the dipole depends upon
the its position with respect to the field,
PE can be defined for magnetic dipole in
the field.
• This PE corresponds to any change in
the rotational configuration.
Comparison with electric
dipole
P
U = - B cos
-PE cos
Monopole does
not exist
Independent of
choice of origin
=xB
Single charge
exists
Only when total
charge vanishes.
=PxE
The field of a
magnetic dipole
Electric field of an electric
dipole
Magnetic field lines of a
magnetic dipole
Bar magnet can also be
considered to be a magnetic
dipole.
Field lines do
not start or end
but
continue
through
the
interior of the
magnets,
forming close
loops.
Similarities
Electric and magnetic dipole fields vary as r-3
when we are far from the dipoles.
Force on a dipole in a
nonuniform field
In a uniform field total force on the dipole
(electric as well as magnetic) is zero.
There is only torque but no net motion
In a non uniform field net force is not
zero. Dipole may move.
dF i2ds B1
Net force
will be
downward
on the loop.
U 2 2B1
U 2 2 z B1z
U 2 2 z B1z
dU
F21
dz
d
F21 2 z B1z
dz
F21 2 z
dB1z
dz
If,
2z 0
dB1 z
0
dz
F21< 0
Force on the loop 2 due to 1 is
attractive (downward).
Induced magnetic
dipole moments
Induced magnetic dipole
moments
• An
applied
magnetic
field can
induce
dipole
moments
I-Iind
I+Iind
Downward
Induced magnetic
dipole moment.
Important points
• In a non uniform magnetic field,
permanent dipoles are attracted
towards the source of the field
• Induced dipoles are repelled from the
source of the field.
• Similar effect is observed in materials
that lack permanent magnetic dipole
moments.
An idea about magnetic
moments
System
Nucleus
Magnetic dipole
Moment (J/T)
~ 10-28
Electron
~ 10-23
Bar Magnet
5
Earth
1022
Atomic and nuclear
magnetism
• Magnetic properties depend upon
magnetic properties of the individual
atoms.
• Magnetic material is consists of atomic
dipoles
dipole moment
associated with circulation of electron.
Calculation
• We consider magnetic materials to be
composed of a collection of atomic
dipoles.
• These dipoles might align when an
external electric field is applied.
• An electron circulating about the
nucleus can be considered as a current
loop of radius r and speed v.
Calculation
• Current in the loop =
q
qv
i
T 2r
ev
evr
2
iA
r
2r
2
• Bohr’s model
• Orbital magnetic dipole moment
nh
mvr
2
el
l
2m
Bohr’s magneton
• This is a basic unit of atomic
magnetic dipole moment
ev
evr
2
iA
r
2r
2
nh
mvr
2
eh
24
B
9.27 10 J / T
4m
Nuclear magnetism
Nuclear
magnetic
moments
Orbital part
Intrinsic part
(spin)