1. Chapter 3a Magnetostatic
ECT1026 Field Theory
Chapter 3a
Magnetostatic
By Dr Mardeni Roslee

2. Contents
3.1 Introduction
3.2 Magnetic Force
3.3 The Biot-Savart Law
3.4 Ampère’s Law

3. Basic Concepts and Quantities
ECT1026 Field Theory
Lecture 3-1
2009/2010
3.1 Introduction
Basic Concepts and Quantities
of Magnetostatics
Current Carrying Conductor
Magnetic Field or Magnetic Flux Lines
Right-Hand Screw Rule
Magnetic Flux Density (Wb/m2)
Magnetic Field Intensity (A/m)
Current & Current Density
Magnetic Dipoles & Current Loops

4. Magnetostatics steady motion of electric charges
ECT1026 Field Theory
3.1 Introduction
Magnetostatics
phenomenon associated with the
steady motion of electric charges
1st Observed Magnetic Phenomena
Natural stone - ancient city of Magnesia
now known as magnetite (Fe3O4)
examples of permanent magnets

5. Permanent Magnets & Compass Needles Interaction
ECT1026 Field Theory
3.1 Introduction
Permanent Magnets & Compass Needles Interaction
described in terms of Magnetic Poles
Point north  North-pole (N) – filed lines emerge
Point south  South-pole (S) – field lines enter S N
Magnetic Poles always exist in Pairs

6. Opposite Poles  Attract
ECT1026 Field Theory
3.1 Introduction S N
Like Poles  Repel N S
Opposite Poles  Attract

7. Chapter 3 Magnetostatics
ECT1026 Field Theory
3.1 Introduction
Chapter 2
Electrostatics
electric charges  electric field
Chapter 3
Magnetostatics
bar magnet  magnetic filed
Magnetic-Field Lines
Magnetic Flux Density B

8. Hans Christian Oersted in 1819 Electric Current  Magnetic Field
ECT1026 Field Theory
3.1 Introduction
Hans Christian Oersted in 1819
Electric Current  Magnetic Field
compass needle was deflected by a current in a wire
The needle always turned in the direction perpendicular to the current-carrying wire and to the radial line connecting the wire to the needle

9. ECT1026 Field Theory
3.1 Introduction
Current-carrying wire induces a magnetic field that formed closed circular loops around the wire

10. Common Effects of Magnetic Field (on Matter)
ECT1026 Field Theory
3.1 Introduction
Common Effects of Magnetic Field (on Matter)
When a current-carrying conductor is placed near to a magnetic needle the needle will deflect
A moving charge particle experiences magnetic force
Any current carrying conductor also experiences a force
Two parallel conductors carrying same direction current are attracted towards each other, and vice versa.

11. Magnetic Field or Magnetic Flux Lines
ECT1026 Field Theory
3.1 Introduction
Characteristics of
Magnetic Field or Magnetic Flux Lines
The distribution and density of magnetic field is visualized as lines of magnetic flux.
Magnetic flux is the basis used to explain magnetic effects and magnitudes
Direction of magnetic field/lines – direction of the north-seeking pole of a compass needle placed in the field
Each line of magnetic flux forms a closed-loop

12. Magnetic Field or Magnetic Flux Lines
ECT1026 Field Theory
3.1 Introduction
Characteristics of
Magnetic Field or Magnetic Flux Lines
Lines of magnetic flux never intersect
Lines of magnetic flux always trying to shorten themselves causing unlike poles to attract each other
Lines of magnetic flux (parallel) are in the same direction and repel each other. They exerted a lateral pressure on one another
A piece of soft iron can be magnetized thru’ magnetic induction

13. ECT1026 Field Theory
3.1 Introduction
Magnetic
Flux, B
lines of force
The magnetic field consists of lines of force, which form complete circles around the conductor
These circles centered around the center of the current carrying conductor and the circular planes are perpendicular to it

14. direction of the circling magnetic flux around the conductor
ECT1026 Field Theory
3.1 Introduction
Right-Hand Screw Rule
Used to relate the
direction of current flowing in a conductor bar, &
direction of magnetic field circling it B I
Thumb
direction of the current
flowing in the conductor 
Directed OUT
of the paper 
Directed INTO
the page
Fingers
direction of the circling magnetic flux around the conductor

15. Parallel and Anti-Parallel Linear Currents
ECT1026 Field Theory
3.1 Introduction
Parallel and Anti-Parallel Linear Currents
Two current carrying conductors are placed in each other parallel
 each will possess a magnetic field of its own, &
 each will exert a magnetic field on the other conductor
Parallel Linear Current
Anti-Parallel Linear Current
A sign “CROSS” indicates the current is flowing IN along the conductor
A sign “DOT” indicates the current is flowing OUT along the conductor

16. ECT1026 Field Theory
3.1 Introduction
Magnetic Flux Density B (Wb/m2) Magnetic Field Intensity H (A/m)
B = mH = mrmo H
m= mrmo
mo : Permeability of free space (= 4p 10-7 H/m)
mr : relative permeability of the material
1 Wb/m2 = 1 T [Wb = weber; T = tesla]
Relative Permeability mr of some common materials
Diamagnetic
Gold, Silver, Copper, Water mr ~ 1
Paramagnetic
Air, Aluminium, Tungsten, platinum ~ 1
Ferromagmetic
Cobalt ~ 250, Nickel ~ 600: Iron ~ 4,000-5,000:
Mild Steel ~ 2600

17.  • B = 0 B • ds = 0 H • dl = I   H = J
ECT1026 Field Theory
3.1 Introduction
The two fundamental postulates of magnetostatics that specify the divergence and the curl of B in free space are:
Integral Form:
Differential Form:
B • ds = 0
 • B = 0
H • dl = I
  H = J

18. Attributes of Electrostatics & Magnetostatics
ECT1026 Field Theory
3.1 Introduction
Attributes of Electrostatics & Magnetostatics

19. uppercase letter I = steady current
ECT1026 Field Theory
3.1 Introduction
Steady Current & Current Density in a Conductor
Current =
(A)
the rate at which the charge is transported past
a given point in a conducing medium
1 A = transportation of one coulomb of charge in one second = 1 C/s
uppercase letter I = steady current

20. J Δq´=vΔv= vΔlΔs´ Current Density (A/m2) 3.1 Introduction
ECT1026 Field Theory
3.1 Introduction
Current Density
(A/m2) J
Fig. 3-1
(Cos 0 =1)
(4)
The charges are moving with a mean velocity u along the axis of the tube.
Over a period Δt, the chares move a distance Δl = uΔt
The amount of charge that crosses the tube’s cross-sectional surface in time is therefore:
(3)
Distance = velocity x time
Δv= ΔlΔs´
Δq´=vΔv= vΔlΔs´
(2)
(1)

21. More General Case (surface normal is not parallel to u)
ECT1026 Field Theory
3.1 Introduction
(Cos  = 0)
More General Case (surface normal is not parallel to u)
Amount of charge Δq flowing through Δs: OR
Δq=vu•ΔsΔt
Δq=vuΔsΔtcos
= vu•Δs
ΔI = Δt Δq
Corresponding current
ΔI = J • Δs
J = v u 
(A/m2)

22. I dl = Js ds = Jdv 3.1 Introduction
ECT1026 Field Theory
3.1 Introduction
Current sources specified in terms of Js over a surface S, or J over a volume V are related by the following equation:
I dl = Js ds = Jdv
Surface Current Density, Js Volume Current Density, J
The total current flowing across
the surface of the conductor is
The total current crossing the
cross section S of the cylinder is
Js dl l
I =
I =
J• ds s l dl ds S

23. Magnetic Dipoles and Current Loops
ECT1026 Field Theory
3.1 Introduction
Magnetic Dipoles and Current Loops
A current loop with dimensions much smaller that the distance between the loop and the observation point is called a magnetic dipole.
Magnetic Field Pattern is similar to that of a permanent magnetic and a pattern of the electric field of the electric dipole (c)=(a)