Magnetic and Electromagnetic Fields

1
Magnetic and Electromagnetic Fields
2
Magnetic Materials
Iron, Cobalt and Nickel and various other alloys
and compounds made using these three basic
elements
3
Electric Current and Magnetic Field
4
A Few Definitions Related to Electromagnetic Field

• (Unit is Weber (Wb)) Magnetic Flux Crossing a
  Surface of
• Area A in m2.

B (Unit is Tesla (T)) Magnetic Flux Density
?/A
H (Unit is Amp/m) Magnetic Field Intensity
? permeability ?o ?r
?o 4?10-7 H/m (H ?Henry) Permeability of
free space (air)
?r Relative Permeability
?r gtgt 1 for Magnetic Material
5
Ampéres Law
The line integral of the magnetic field intensity
around a closed path is equal to the sum of the
currents flowing through the area enclosed by
the path.
6
Example of Ampéres Law
Find the magnetic field along a circular path
around an infinitely long Conductor carrying I
ampere of current.
Since both
are perpendicular to radius r at any point A
and
on the circular path, the angle ? is zero between
them at all points. Also since all the points on
the circular path are equidistant from the
current carrying conductor is constant at
all points on the circle
or
7
Magnetic Circuits

• They are basically ferromagnetic
  structures(mostly Iron, Cobalt,
• Nickel alloys and compounds) with coils wound
  around them
• Because of high permeability most of the magnetic
  flux is confined
• within the magnetic circuit
• Thus is always aligned with
• Examples Transformers,Actuators, Electromagnets,
  Electric Machines

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Magnetic Circuits (1)
w
I
N
d
l mean length
9
Magnetic Circuits (2)
F NI Magneto Motive Force or MMF of turns
Current passing through it
F NI Hl (why!)
or
or
or
or
Reluctance of magnetic path
10
Analogy Between Magnetic and Electric Circuits
F MMF is analogous to Electromotive force (EMF)
E
Flux is analogous to I Current
Reluctance is analogous to R Resistance
Permeance
Analogous to conductance
11
Examples of Magnetic Circuits On Greenboard
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Inductance(L)
Definition Flux Linkage(?) per unit of
current(I) in a magnetic circuit
I
N
Thus inductance depends on the geometry of
construction
13
Example of Inductance of Magnetic Circuit On
Greenboard
14
Faradays law of Electromagnetic Induction
The EMF (Electromotive Force) induced in a
magnetic circuit is Equal to the rate of change
of flux linked with the circuit
15
Lenzs Law
The polarity of the induced voltage is given by
Lenzs law
The polarity of the induced voltage will be such
as to oppose the very cause to which it is due
Thus sometimes we write
16
A precursor to Transformer
? ?m Sin(?t)
V Vm Cos(?t)
Ideally

17
A Precursor to Transformer(2)
time
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Self Inductance, Mutual inductance and Leakage
Flux
?12 ?21 ?m
Mutual Flux
i1
i2
?22
?11
Leakage Flux
N2
N1
Coil 2
Coil 1
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Self ,Leakage and Mutual Flux
?11 is the leakage flux of coil 1. This flux
does not link coil 2 and links only coil
1. Similarly ?22 is the leakage flux of coil 2.
This flux does not link coil 1 and links only
coil 2. ?12 ?21 ?m is the mutual flux that
links both coil 1 and 2 Then Self flux of coil
1 is ?1 ?11 ?12 ?11 ?m Then Self flux of
coil 2 ?2 ?22 ?21 ?22 ?m
20
Self Inductance
Definition Total flux linked by a coil per unit
of its own current
Self flux linking coil 1 is ?11N1?1 N1(?11
?12) Self flux linking coil 2 is ?22 N2?2
N2(?22 ?21)
L1Self Inductance of coil 1
L2Self Inductance of coil 2
A coil always links all the flux it produces
21
Mutual Inductance
Definition Portion of flux produced by one coil
(say 2) that links the other coil (say 1) per
unit of current in the flux producing coil (coil
2).
M12Mutual Inductance of coil 1 due to current in
coil 2
M21Mutual Inductance of coil 2 due to current in
coil 1
Normally M12 M21 M
22
Relationship between Mutual and Self Inductance

Let
and
Then
is the coefficient of coupling
Where
or
Normally k lt 1 (meaning leakage flux cannot be
avoided in practice)
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Dot Convention
The dots are placed in such a manner that the
currents entering (or leaving) both the dotted
terminals will produce adding magnetic flux. In
this case the mutual flux linkages will add to
the self flux linkages.(Case I) Conversely, if
current enters through one dotted terminal and
leaves through the other, they produce opposing
flux. In this case mutual flux linkages subtract
from self linkages.(Case II)
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Case I
e1
e2
25
Case II
e1
e2
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Extension of Dot Convention
The dot convention also implies that current
entering ( increasing) in one dotted terminal
will cause current to come out of the other
terminal ( increasing)
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Example on Dot Convention on Greenboard
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Iron Losses in Magnetic Circuit

• There are two types of iron losses
• Hysteresis losses
• Eddy Current Losses

Total iron loss is the sum of these two losses
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Hysteresis losses
i
f frequency of sine source
B
i
B-H or Hysteresis loop
saturation
Br
knee point
5
4
2
t
0
1
3
2
1
3
H
Hc
4
5
Br Retentive flux density (due to property of
retentivity) Hc Coercive field intensity (due to
property of coercivity)
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Hysteresis losses (2)

• In each of the current cycle the energy lost in
  the core is
• proportional to the area of the B-H loop
• Energy lost/cycle Vcore

khBnmaxf

• Ph Hysteresis loss f Vcore

kh Constant Bmax Peak flux density
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Eddy current loss
Laminations
flux
flux
Current
Because of time variation of flux flowing through
the magnetic material as shown, current is
induced in the magnetic material, following
Faradays law. This current is called eddy
current. The direction of the current is
determined by Lenzs law. This current can be
reduced by using laminated (thin sheet) iron
structure, with Insulation between the
laminations.

• Pe Eddy current loss

keB2maxf2
,
Bmax Peak flux density
kh Constant