1
ةيدوعسلا ةيبرعلا ةكلمملا
ةيملاسلإا دوعس نب دمحم ماملإا ةعماج
مولعلا ةيلك
ءايزيفلا مسق
KINGDOM OF SAUDI ARABIA
AL

IMAM MUHAMMAD BIN SAUD
ISLAMIC UNIVERSITY
FACULTY OF SCIENCES
DEPARTMENT OF PHYSICS
Dr. Naglaa
Fathy
Mohamed
Physics department
1433/1434
2
Chapter
1
:
Electrostatic Fields
Chapter
3
:
Magnetic Fields in Matter
Chapter 2
: Electric Fields in Matter
Chapter
4
:
Maxwell’s Equations
Chapter 5
:
Electromagnetic Wave Propagation
Elements of
Electromagnetics

Third Edition
–
Matthew N. O.
Sadiku
.
3
Chapter
3
Magnetic Field in Matter
Chapter Outline:
1
.
Volume Current Density
2
.
Biot

Savart’s
Law
3
.
Ampere’s Circuit Law

Maxwell’s Equation
4
.
Magnetic Flux Density
–
Maxwell’s Equation
5
.
Maxwell’s Equations for Static Electromagnetic Field
6
.
Magnetic Dipole
7
.
Magnetization in Materials
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
4
The
net magnetic flux
(
Wb
) through surface S
is
given by.
In
free
space, the magnetic flux density is given by:
4

Magnetic Flux
Density
–
Maxwell’s Equation
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
5
4

Magnetic Flux
Density
–
Maxwell’s Equation
The total flux through a closed surface in a magnetic field must be zero
o
An
isolated magnetic charge does not exist
o
Magnetic flux is conserved
By applying the divergence theorem:
Fourth Maxwell's
equation
This Equation suggests that the magnetic field lines are always continuous.
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY 321
5

Maxwell’s Equations for Static
Electromagnetic Fields
Maxwell's four equations for
static electromagnetic fields
Maxwell's equations are only for static EM fields.
6
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY 321
7
6

Magnetic Dipole

A small filamentary current loop or a bar magnet is usually referred
to as a magnetic dipole.

The direction of the magnetic dipole moment points from the south to
north pole of a magnet.
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY 321
8
6

Magnetic Dipole
Magnetic field at P due to a current loop:
Magnetic dipole moment
A bar magnet is usually referred to as a
magnetic dipole.
9
7

Magnetization in Materials
Electron orbiting
around the nucleus
Orbital magnetic moment
Spin magnetic moments
Magnetic
Moments
of
Atoms
:
•
Both of these electronic motions produce internal magnetic fields B.
o
Similar to the magnetic field produced by a current loop
10
7

Magnetization in Materials
The magnetic dipole moment of the loop:
where S is the area of the loop and I is the bound current (bound to the atom).
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY 321
11
7

Magnetization in Materials
Without an external magnetic field applied to
the material, the sum of magnetic dipole
moments is zero due to the random orientation.
Dr. Naglaa fathy. Electromagnetic
Field, PHY
321
12
7

Magnetization in Materials
When an external magnetic field is applied, the
magnetic moments of the electrons align themselves
with magnetic field so that the net magnetic moment is
not zero.
Dr. Naglaa fathy. Electromagnetic Field, PHY
321
13
7

Magnetization in Materials
•
The relation between Magnetization (M) and applied external magnetic field:
(a) Diamagnetic materials
(b) Paramagnetic materials
(c) Ferromagnetic Materials
Classification of magnetic Materials:
H
paramagnetic
H
Diamagnetic
H
=0
Ferromagnetic
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
Magnetic Domains:
K
L
M N
electrons in Fe atom:
Dr.
Naglaa
Fathy
Mohamed, physics department
15
7

Magnetization in Materials
The magnetization (in A/m
) is
:
the magnetic dipole moment per unit volume.
If there are N atoms in a given volume
A medium for which M is not zero everywhere is said to be magnetized.
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
16
7

Magnetization in Materials
The potential of a magnetic body is due to:
•
volume current density
J
b
throughout the body and
•
surface
current
K
b
on the surface of the body.
For a magnetized body
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
17
7

Magnetization in Materials
•
J is the free current volume density
In free space, M = 0:
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
18
7

Magnetization in Materials
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
19
7

Magnetization in Materials
m
is a dimensionless quantity
called
magnetic susceptibility
of the
medium.
o
is a measure of how susceptible (or sensitive) the material is to a
magnetic field
Dr.
Naglaa
fathy
. Electromagnetic Field, PHY
321
20
7

Magnetization in Materials
•
>
0
paramagnet
•
<
0
Diamagnetic
:
permeability of the
Material (
henrys/meter)
r
: relative
permeability of
the material
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