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

yjshin@chosun.ac.kr 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