Chapter 7. Magnetic Field
PART 2
PART 1 A. Magnetism
B. Magnetostatic Field
C. Magnetic Potential and Potential Gradient
D. Magnetic Dipole and Magnetic Shell
E. Current-produced Magnetic Fields
F. Electrodynamic Force in the Magnetic Field
G. Special Phenomenon of Electromagnetic Force
Chapter 7. Magnetic Field
[email protected] www.chosun.ac.kr/~yjshin
A. Magnetism
B. Magnetostatic Field
C. Magnetic Potential and
Magnetic Potential Gradient
D. Magnetic Dipole and Magnetic Shell
Yong-Jin Shin, Professor of Physics, Chosun University
PART 1
7.A. Magnetism
◈ Magnetism
Magnetic phenomena were first observed
at least 2500 years ago in fragments of
magnetized iron are found near the
ancient city of Magnesia (now in western
Turkey)
The first evidence of the relationship of
magnetism to moving charges was
discovered in 1820 by the Oersted.
Magnesia city → Magnetism → Permanent Magnet
Current-carrying wire → Deflect needle of compass
Magnetic Phenomenon
Its north geographic pole is close to a
magnetic south pole, which is why the north
pole of a compass needle points north.
Magnetic filed lines, show the direction that
a compass would point at each location.
The field, which is caused by currents in the
earth’s molten core, changes with time.
Magnetic Phenomenon
(a), (b) : two bar magnets attract when
opposite poles (N and S, or S and N) are
next to each other.
(c), (d) : the bar magnets repel when like
poles (N and N, or S and S) are next to each
other.
◈ Permanent magnets were found to exert forces on each other.
◈ The earth itself is a magnet.
◈ Existence of an isolated magnetic monopole ?
Breaking a bar magnet.
Each piece has a norgth
and south pole, even if the
pieces are different sizes.
(The smaller the piece, the
weaker its magnetism) …… yields three magnets,
not three isolated poles
Breaking a magnet in three ……
Static charge (electrostatic)
Moving charge (current)
Source of Electric Field
Source of Magnetic Field
Electric Charge
Magnetic Charge
Electric Dipole
Magnetic Dipole
Magnetic Phenomenon
◈ Magnetic Induction
• A phenomenon that the objects (ex; nail or pin) under the influence of
a magnet is a magnet temporary.
- Objects that have been magnetized. → Magnetization
- Objects become a magnet → magnetic material (cf; non-magnetic material)
• Residual magnetism of magnetic material
- Instant magnet : residual magnetism is unstable to spatial and temporal
(ex; soft steel)
- Permanent magnet : Stable residual magnetism (ex; hard steel)
Magnetic Induction Effect
magnet magnet
magnet
◈ Magnetic field and magnetic pole
• Magnetic field : an area around a magnet, in which the magnet’s power
to attract things is felt.
• Unit of magnetic pole : 1[Wb] the unit magnetic pole; the strength that
would cause a unit magnetic pole to experience a force of 6.33×104[N]
between the same magnitude of poles ( m1 =m2 ) per meter in a free space.
◈ Force between two magnetic pole (Coulomb’s Law; 1785)
Nr
mm
r
mm
r
mmkF
2
214
2
21
0
2
21 1033.64
1
]/[10257.1104 67
0 mH permeability of free space :
Q. 7.1
Coulomb’s Law for Magnetic Pole
(a) like poles (m1m2>0) repel F (b) unlike poles (m1m2<0) attract F
▷ Electrostatic Force
K 8.9876 109 9 109 (N ·m2/C2 ) 107 c2
4o 1
o 8.854 1012 9 109 (C2 / N·m2 )
“permittivity constant”
107
4c2
F K Q1Q2
r 2
F 9 109 ( N ) Q1Q2
r 2
Q1Q2
r 2 4o 1
FIG. 2-5. Coulomb’s Law
attraction
repulsion
The magnitude of the electric force between two point
charges is directly proportional to the product of the
charges and inversely proportional to the square of
the distance between them.
Coulomb’s Law for Electric Charge (Ch.2)
7.B. Magnetostatic Field
Magnetic Field Lines
◈ Properties of magnetic field lines
① It is an imaginary line to represents the distribution of the magnetic field.
② Concentrated near the magnetic pole, and scattered away from the pole.
③ Magnetic field lines are listed from the N pole to the S pole.
④ The tangent line of magnetic field lines is the direction of the magnetic field
at that point.
⑤ Magnetic field lines repel each other.
⑥ The density of magnetic field lines represents the intensity of magnetic
field at that point.
• The polarization P and the magnetization M have the same magnitude and
direction everywhere within their respective cylinders.
• E directed to the left.
• E is discontinuous at the end of
the cylinder surface.
• B directed to the right.
• B is continuous at the end of the
cylinder surface.
• Direction of B suddenly different
at the side of the cylinder surface.
◈ Direction of electric field(E) and magnetic field(B)
E
P
a uniformly polarized cylinder
B
M
a uniformly magnetized cylinder
Magnetic Field Lines
◈ Intensity of magnetic field and Unit
][1
4
1
4
12
0
2
21
0
Nr
m
r
mmF
“Coulomb’s Law”
]/[4
12
0
mATr
mH
“Magnetic field intensity”
• When magnetic pole m [Wb] placed in the magnetic field H[AT/m], the
forces F acting on the here is
Q. 7.2
Intensity of the Magnetic Field
• Intensity of the magnetic field at point
defined as a magnetic mono-pole
receiving force [N] when magnetic
mono-pole (m : +1 Wb) placed at any
point in the magnetic field,
• The unit for the intensity of magnetic field is the [N/Wb] or [AT/m].
mHF m
FH
▷ Intensity of Electric Field
• Intensity of the electric field at point P is E=F/q (q : +1 Coulomb), and
the direction of E is that of the force on the positive test charge.
• The SI unit for the intensity of electric field is the newton/coulomb (N/C)
• We use a positive test charge to define the intensity of electric field of a
charged object, that field intensity exists independently of the test charge.
q
FE
2
04
1
r
qQF
CN
r
Q
r
QE /109
4
12
9
2
0
FIG. 2-7. Intensity of electric field
Intensity of the Electric Field (Chapter 2)
◈ Magnetic field intensity due to a bar-magnet
Repulsion F1 to the point P (+1Wb) by N-pole
]/[4
112
10
1 mATHr
mF
]/[4
122
20
2 mATHr
mF
Therefore, magnetic field intensity at point P is
]/[21 mATHHH
Attraction F2 to the point P (+1Wb) by S-pole
Intensity of the Magnetic Field
Density of Magnetic Field Lines
◈ Density of magnetic field lines = Magnetic field intensity (H)
]/[ 2mWbds
dNH
The density of magnetic field line is defined as the
number of magnetic field line passes perpendicular
to the unit area [m2] in the magnetic field.
◈ Number of magnetic field lines (dN)
][4
104
7
0
2 eamm
rHdsHdN
2
04
1
r
mH
7
0 104 where, &
When magnetic pole +m[Wb] is in a material with relative
permeability μs
][1
0
eam
Ns
s
][4
12
0
Nr
mF
swith
• Regardless of the medium, assuming that one line coming from +1[Wb].
Magnetic flux, it occurs by N- and S-pole.
• Outgoing part of the magnetic flux is N pole, enter part is S pole.
If you have an iron core, prone to magnetic flux.
Magnetic Flux and Flux Density
• It is defined as the number of
magnetic flux passes perpendicular
to the unit area in the magnetic field.
◈ Magnetic Flux
◈ Magnetic Flux Density B
]/[ 2mWbdS
dB
▷ Electric Flux Density
Electric flux density is amount of the electric flux per unit area.
SD
FIG. 2-12. Electric Flux Density:
Electric Flux (Chapter 2)
Electric Flux Density
]/[ 2mCdS
dD E
]/[ 2mWbdS
dB M
Magnetic Flux Density
Electric Displacement D
Electric Field Intensity E
D = E : permittivity
Magnetic Induction B
Magnetic Field Intensity H
B = H : permeability