This document provides an overview of magnetostatics and key concepts related to magnetism. It begins with a top ten list of magnetism principles. It then discusses the properties of magnetic poles, fields, and materials. Key points made include that every magnet has both a north and south pole, magnetic fields are generated by moving charges, and materials can be classified based on their magnetic permeability. The document also introduces critical magnetism concepts such as the Biot-Savart law, Ampere's law, magnetic dipoles, and the forces and energy associated with magnetic fields.

1. MAGNETOSTATICS
KONGUNADU COLLEGE OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF ELECTRICALAND ELECTRONICS ENGINEERING
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2. Top Ten List
1. There are North Poles and South Poles.
2. Like poles repel, unlike poles attract.
3. Magnetic forces attract only magnetic materials.
4. Magnetic forces act at a distance.
5. While magnetized, temporary magnets act like permanent magnets.
What We Will Learn About Magnetism
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3. Top Ten continued
6. A coil of wire with an electric current flowing through it becomes a
magnet.
7. Putting iron inside a current-carrying coil increases the strength of the
electromagnet.
8. A changing magnetic field induces an electric current in a conductor.
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4. Top Ten Continued
9. A charged particle experiences no magnetic force when moving
parallel to a magnetic field, but when it is moving perpendicular to
the field it experiences a force perpendicular to both the field and the
direction of motion.
10. A current-carrying wire in a perpendicular magnetic field
experiences a force in a direction perpendicular to both the wire and
the field.
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5. For Every North, There is a South
Every magnet has at least one north pole and one south pole. By
convention, we say that the magnetic field lines leave the North end of a
magnet and enter the South end of a magnet.
If you take a bar magnet and break it into two pieces, each piece will again
have a North pole and a South pole. If you take one of those pieces and
break it into two, each of the smaller pieces will have a North pole and a
South pole. No matter how small the pieces of the magnet become, each
piece will have a North pole and a South pole.
S N S N S N
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6. No Monopoles Allowed
It has not been shown to be possible to end up with a single North
pole or a single South pole, which is a monopole ("mono" means one
or single, thus one pole).
Note: Some theorists believe that magnetic monopoles may have
been made in the early Universe. So far, none have been detected.
S N
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7. Magnets Have Magnetic Fields
We will say that a moving charge sets up in the space around it a
magnetic field,
and
it is the magnetic field which exerts a force on any other charge
moving through it.
Magnetic fields are vector quantities….that is, they
have a magnitude and a direction!
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8. Defining Magnetic Field Direction
Magnetic Field vectors as written as B
Direction of magnetic field at any point is defined as
the direction of motion of a charged particle on which
the magnetic field would not exert a force.
Magnitude of the B-vector is proportional to the force
acting on the moving charge, magnitude of the moving
charge, the magnitude of its velocity, and the angle
between v and the B-field. Unit is the Tesla or the Gauss (1
T = 10,000 G).
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9. Scientists Can Be Famous, Too!
Tesla
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10. Famous, continued
Gauss
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11. The Concept of “Fields”
A magnet has a
‘magnetic field’
distributed throughout
the surrounding space
Michael Faraday
realized that ...
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12. Magnetics
 A magnet attracts or repels another magnet – this
gives us the first observable interaction in the
magnetic field –it also attracts a piece of iron.
 It will not attract a piece of copper.
 Conclusion: there are different types of material in
terms of their magnetic properties.
 Magnetic properties are governed by the
permeability of the material,  [henry/meter]
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13. Magnetics
 The strength of the magnetic field is usually given
by the magnetic flux density B [tesla]
 The magnetic flux density is also called magnetic
induction
 The magnetic field intensity H [ampere/meter].
 The relation between the two is simple:
B =0rH
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14. Magnetics
 0=4x10 [H/m] is the permeability of vacuum
 r is the relative permeability of the medium in
which the relation holds,
 r is given as the ratio between the permeability of
the medium and that of vacuum
 A dimensionless quantity associated with each
material in nature.
 Permeabilities of some useful materials are given
next.
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15. Magnetics
 Magnetic materials:
 Diamagnetic, r < 1
 Paramagnetic r > 1
 Ferromagnetic r >> 1 (iron-like)
 The latter are often the most useful materials when
working with magnetic fields.
 There are other types of magnetic materials
(ferrites, magnetic powders, magnetic fluids,
magnetic glasses, etc.)
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16. Magnetization curve and
permeability of ferromagnetic
materials
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17. Currents, fields and flux
 Relation between current and magnetic
flux density.
 For a long straight wire carrying a current
I and placed in a medium of permeability
0r. The magnitude of the magnetic
flux density is:
 r is the distance from the wire to the location
where the field is calculated
 the magnetic field is a vector and has a
direction (next) - field is perpendicular to I
B = 0r
I
2r
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18. Relation between current and
magnetic field
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19. Magnetic flux
 Flux is the integral of flux
density over an area S:
 Unit of flux is the weber [Wb]
 1 [Wb] = 1 [Tm2]
 Flux relates to power and
energy in the magnetic field
 = B.ds
S
Wb
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20. Force in the magnetic field
 Force in a magnetic field is
based on the fact that a charge
moving at a velocity v in a
magnetic field B experience a
force (called the Lorentz force)
given as:
 vB is the angle between the
direction of motion and the
direction of B
 F is perpendicular to both v and
B as shown (next).
F= qvBsinvb [N]
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21. Relation between charge, current
and force in a magnetic field
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22. Ampere’s Law of Force (Cont’d)
 Experimental facts:
 Two parallel wires
carrying current in
the same direction
attract.
 Two parallel wires
carrying current in
the opposite
directions repel.
 
I1 I2
F12F21
 
I1 I2
F12F21
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23. Ampere’s Law of Force (Cont’d)
 Experimental facts:
 A short current-
carrying wire
oriented
perpendicular to a
long current-
carrying wire
experiences no force.

I1
F12 = 0
I2
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24. Forces on currents For long parallel wires, the force for a length L of
the wire is: F = BIL
 For other configuration the relation is much
more complicated but force is proportional to B, I
and L.
 A single wire carrying a current will be attracted
or repelled by a permanent magnet
 These principles are the basis for magnetic
actuation
 Forces can be very large since B, I and L can be
controlled and can be quite large.
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25. Inductance
 Defined as the ratio of flux and the
current that produced is:
 Inductance is independent of
current since  is current
dependent
 All magnetic devices have an
inductance but inductance is most
often associated with coils
L = 
I
webber
ampere
or[henry]
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26. Inductance
 Two types of inductance:
 1. Self inductance: the ratio of the flux produced by a
circuit (a conductor or a coil) in itself and the current that
produces it. Usually denoted as Lii.
 2. Mutual inductance: the ratio of the flux produced by
circuit i in circuit j and the current in circuit i that
produced it. Denoted as Mij.
 A mutual inductance exists between any two circuits as
long as there a magnetic field (flux) that couples the two.
 This coupling can be large (tightly coupled circuits) or
small (loosely coupled circuits).
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27. Self and mutual inductance
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28. Magnetic Flux Density
 where



1
12
2
12
110
12
ˆ
4 C
R
R
aldI
B


the magnetic flux density at the location of
dl2 due to the current I1 in C1
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29. Magnetic Flux Density (Cont’d)
 Suppose that an infinitesimal current
element Idl is immersed in a region of
magnetic flux density B. The current
element experiences a force dF given by
BlIdFd 
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30. Magnetic Flux Density (Cont’d)
 The total force exerted on a circuit C
carrying current I that is immersed in a
magnetic flux density B is given by
 
C
BldIF
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31. Force on a Moving Charge
 A moving point charge placed in a
magnetic field experiences a force given
by
BvQ
The force experienced
by the point charge is
in the direction into the
paper.
BvQFm  vQlId 
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32. The Biot-Savart Law
 The Biot-Savart law gives us the B-field arising at a
specified point P from a given current distribution.
 It is a fundamental law of magnetostatics.
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33. The Biot-Savart Law (Cont’d)
 The contribution to the B-field at a point P
from a differential current element Idl’ is
given by
3
0
4
)(
R
RldI
rBd




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34. Ampere’s Circuital Law in Integral
Form Ampere’s Circuital Law in integral form
states that “the circulation of the magnetic
flux density in free space is proportional to
the total current through the surface
bounding the path over which the
circulation is computed.”
encl
C
IldB 0
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35. Ampere’s Circuital Law in Integral
Form (Cont’d)
By convention, dS is
taken to be in the
direction defined by the
right-hand rule applied
to dl.
 
S
encl sdJI
Since volume current
density is the most
general, we can write
Iencl in this way.
S
dl
dS
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36. Applying Stokes’s Theorem to
Ampere’s Law




S
encl
SC
sdJI
sdBldB
00 
 Because the above must hold for any
surface S, we must have
JB 0
Differential form
of Ampere’s Law
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37. Magnetic Dipole
 A magnetic dipole comprises a small
current carrying loop.
 The point charge (charge monopole) is the
simplest source of electrostatic field. The
magnetic dipole is the simplest source of
magnetostatic field. There is no such
thing as a magnetic monopole (at least as
far as classical physics is concerned).
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38. Magnetic Dipole (Cont’d)
 The magnetic dipole is analogous to the electric
dipole.
 Just as the electric dipole is useful in helping us to
understand the behavior of dielectric materials, so the
magnetic dipole is useful in helping us to understand
the behavior of magnetic materials.
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39. Boundary Conditions
 Within a homogeneous
medium, there are no
abrupt changes in H or
B. However, at the
interface between two
different media (having
two different values of
), it is obvious that one
or both of these must
change abruptly.
1
2
naˆ
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40. Boundary Conditions (Cont’d)
 The normal component of a solenoidal
vector field is continuous across a material
interface:
 The tangential component of a conservative
vector field is continuous across a material
interface:
nn BB 21 
0,21  stt JHH
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41. Torque on a Current Carrying Loop
 The torque acting on the loop tries to align the
magnetic dipole moment of the loop with the B field
BmT 
holds in general
regardless of
loop shape
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42. Energy Stored in an Inductor
 The magnetic energy stored in an inductor is given by
2
2
1
LIWm 
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