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# Electromagnetism - Magnetic Materials Mechanical Engineering Notes | EduRev

## Mechanical Engineering : Electromagnetism - Magnetic Materials Mechanical Engineering Notes | EduRev

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Electromagnetism - Lecture 10
Magnetic Materials
 Magnetization Vector M
 Magnetic Field Vectors B and H
 Magnetic Susceptibility & Relative Permeability
 Diamagnetism
 Paramagnetism
 Eects of Magnetic Materials
1
Page 2

Electromagnetism - Lecture 10
Magnetic Materials
 Magnetization Vector M
 Magnetic Field Vectors B and H
 Magnetic Susceptibility & Relative Permeability
 Diamagnetism
 Paramagnetism
 Eects of Magnetic Materials
1
Introduction to Magnetic Materials
There are three main types of magnetic materials with dierent
magnetic susceptibilities,
M
:
 Diamagnetic - magnetization is opposite to external B

M
is small and negative.
 Paramagnetic - magnetization is parallel to external B

M
is small and positive.
 Ferromagnetic - magnetization is very large and non-linear.

M
is large and variable.
Can form permanent magnets in absence of external B
) In this lecture Diamagnetism & Paramagnetism
Ferromagnetism will be discussed in Lecture 12
2
Page 3

Electromagnetism - Lecture 10
Magnetic Materials
 Magnetization Vector M
 Magnetic Field Vectors B and H
 Magnetic Susceptibility & Relative Permeability
 Diamagnetism
 Paramagnetism
 Eects of Magnetic Materials
1
Introduction to Magnetic Materials
There are three main types of magnetic materials with dierent
magnetic susceptibilities,
M
:
 Diamagnetic - magnetization is opposite to external B

M
is small and negative.
 Paramagnetic - magnetization is parallel to external B

M
is small and positive.
 Ferromagnetic - magnetization is very large and non-linear.

M
is large and variable.
Can form permanent magnets in absence of external B
) In this lecture Diamagnetism & Paramagnetism
Ferromagnetism will be discussed in Lecture 12
2
Magnetization Vector
The magnetic dipole moment of an atom can be expressed as an
integral over the electron orbits in the Bohr model:
m =
Z
atom
IA^ z
The current and magnetic moment of the i-th electron are:
I =
ev
i
2r
i
m
i
= IA^ z =
e
2m
e
L
i
The magnetic dipole density is the magnetization vector M:
M =
dm
d
= N
A
e
2m
e
< L
i
>
atom
This orbital angular momentum average is also valid in quantum
mechanics
3
Page 4

Electromagnetism - Lecture 10
Magnetic Materials
 Magnetization Vector M
 Magnetic Field Vectors B and H
 Magnetic Susceptibility & Relative Permeability
 Diamagnetism
 Paramagnetism
 Eects of Magnetic Materials
1
Introduction to Magnetic Materials
There are three main types of magnetic materials with dierent
magnetic susceptibilities,
M
:
 Diamagnetic - magnetization is opposite to external B

M
is small and negative.
 Paramagnetic - magnetization is parallel to external B

M
is small and positive.
 Ferromagnetic - magnetization is very large and non-linear.

M
is large and variable.
Can form permanent magnets in absence of external B
) In this lecture Diamagnetism & Paramagnetism
Ferromagnetism will be discussed in Lecture 12
2
Magnetization Vector
The magnetic dipole moment of an atom can be expressed as an
integral over the electron orbits in the Bohr model:
m =
Z
atom
IA^ z
The current and magnetic moment of the i-th electron are:
I =
ev
i
2r
i
m
i
= IA^ z =
e
2m
e
L
i
The magnetic dipole density is the magnetization vector M:
M =
dm
d
= N
A
e
2m
e
< L
i
>
atom
This orbital angular momentum average is also valid in quantum
mechanics
3
Notes:
Diagrams:
4
Page 5

Electromagnetism - Lecture 10
Magnetic Materials
 Magnetization Vector M
 Magnetic Field Vectors B and H
 Magnetic Susceptibility & Relative Permeability
 Diamagnetism
 Paramagnetism
 Eects of Magnetic Materials
1
Introduction to Magnetic Materials
There are three main types of magnetic materials with dierent
magnetic susceptibilities,
M
:
 Diamagnetic - magnetization is opposite to external B

M
is small and negative.
 Paramagnetic - magnetization is parallel to external B

M
is small and positive.
 Ferromagnetic - magnetization is very large and non-linear.

M
is large and variable.
Can form permanent magnets in absence of external B
) In this lecture Diamagnetism & Paramagnetism
Ferromagnetism will be discussed in Lecture 12
2
Magnetization Vector
The magnetic dipole moment of an atom can be expressed as an
integral over the electron orbits in the Bohr model:
m =
Z
atom
IA^ z
The current and magnetic moment of the i-th electron are:
I =
ev
i
2r
i
m
i
= IA^ z =
e
2m
e
L
i
The magnetic dipole density is the magnetization vector M:
M =
dm
d
= N
A
e
2m
e
< L
i
>
atom
This orbital angular momentum average is also valid in quantum
mechanics
3
Notes:
Diagrams:
4
Magnetization Currents
The magnetization vector M has units of A/m
The magnetization can be thought of as being produced by a
magnetization current density J
M
:
I
L
M:dl =
Z
A
J
M
:dS J
M
=r M
For a rod uniformly magnetized along its length the magnetization
can be represented by a surface magnetization current
owing
round the rod:
J
S
= M ^ n
The distributions J
M
and J
S
represent the eect of the atomic
magnetization with equivalent macroscopic current distributions
5
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