Download Lecture 16a_Electromagnetic 1

Electromagnetic
Define and explain Faraday Law, Flemming Law,
magnetic field, magnetik material, Magnetisation
curve
Define and explain magnetic equivalent circuit,
electromagnetic induction, Sinusoidal excitation,
Lenz’s law.
Analyze and explain magnetic losses, eddy
current, hysterisis
CHAPTER 11
MAGNETIC FIELDS
11.2 Magnetic Fields
In the region surrounding a permanent
magnet there exists a magnetic field, which
can be represented by magnetic flux lines
similar to electric flux lines.
Magnetic flux lines differ from electric flux
lines in that they don’t have an origin or
termination point.
Magnetic flux lines radiate from the north pole
to the south pole through the magnetic bar.
11.2 Magnetic Fields
Flux distribution for a permanent magnet
11.2 Magnetic Fields
Continuous magnetic flux lines will strive to
occupy as small an area as possible.
The strength of a magnetic field in a given
region is directly related to the density of flux
lines in that region.
If unlike poles of two permanent magnets are
brought together the magnets will attract, and
the flux distribution will be as shown below.
11.2 Magnetic Fields
Flux distribution for two adjacent, opposite poles
11.2 Magnetic Fields
If like poles are brought together, the magnets
will repel, and the flux distribution will be as
shown.
11.2 Magnetic Fields
If a nonmagnetic material, such as glass per,
is placed in the flux paths surrounding a
permanent magnet, there will be an almost
unnoticeable change in the flux distribution.
If a nonmagnetic material, such as copper, is
placed in the flux paths surrounding a
permanent magnet, there will be an almost
noticeable change in the flux distribution.
11.2 Magnetic Fields
11.2 Magnetic Fields
This principle is put to use in the shielding of
sensitive electrical elements and instruments
that can be affected by stray magnetic fields.
11.2 Magnetic Fields
A current-carrying conductor develops
magnetic fields in the form of concentric circle
around it.
11.2 Magnetic Fields
If the coil is wound in a single-turn coil, the
resulting flux flows in a common direction
through the centre of the coil.
11.2 Magnetic Fields
A coil of more than one turn produces a
magnetic field that exists in a continuous path
through and around the coil.
11.2 Magnetic Fields
The flux distribution around the coil is quite
similar to the permanent magnet.
The flux lines leaving the coil from the left and
entering to the right simulate a north and a
south pole.
The concentration of flux lines in a coil is less
than that of a permanent magnet.
11.2 Magnetic Fields
The field concentration (or field strength) may
be increased effectively by placing a core
made of magnetic materials (e.g. iron, steel,
cobalt) within the coil – electromagnet.
11.2 Magnetic Fields
The field strength of an electromagnet can be
varied by varying one of the component
values (i.e. currents, turns, material of the
core etc.)
11.2 Magnetic Fields
The direction of the magnetic flux lines can
be found by placing the thumb of the right
hand in the direction of conventional current
flow and noting the direction of the fingers
(commonly called the right hand rule).
11.2 Magnetic Fields
11.2 Magnetic Fields
Flux and Flux Density
In the SI system of units, magnetic flux is
measured in webers (Wb) and is represented
using the symbol .
Wilhelm Eduard Weber (1804 – 1891)
Prof. of Physics, University of Göttingen
11.2 Magnetic Fields
The number of flux lines per unit area is
called flux density (B). Flux density is
measured in teslas (T).
Its magnitude is determined by the following
equation:
1 tesla = 1 T = 1 Wb/m2
Nikola Tesla (1856 – 1943)
Electrical Engineer and Inventor
Recipient of the Edison Medal in 1917.
11.2 Magnetic Fields
• The flux density of an electromagnet is
directly related to:
•
the number of turns of
•
the current through
the coil
The product is the magnetomotive force:
  NI
ampere - turns, At 
11.2 Magnetic Fields
Permeability
Another factor affecting the field strength is
the type of core used.
If cores of different materials with the same
physical dimensions are used in the
electromagnet, the strength of the magnet will
vary in accordance with the core used.
The variation in strength is due to the number
of flux lines passing through the core.
11.2 Magnetic Fields
Magnetic material is material in which flux
lines can readily be created and is said to
have high permeability.
Permeability () is a measure of the ease
with which magnetic flux lines can be
established in the material.
11.2 Magnetic Fields
Permeability of free space 0 (vacuum) is
o  4 10 7 Wb/A.m 
Materials that have permeability slightly
less than that of free space are said to be
diamagnetic and those with permeability
slightly greater than that of free space are
said to be paramagnetic.
11.2 Magnetic Fields
Magnetic materials, such as iron, nickel,
steel and alloys of these materials, have
permeability hundreds and even thousands
of times that of free space and are referred
to as ferromagnetic.
The ratio of the permeability of a material to
that of free space is called relative
permeability:

r 
o
11.2 Magnetic Fields
In general for ferromagnetic materials,
r  100
For nonmagnetic materials,
r  1
Relative permeability is a function of
operating conditions.
11.4 Induced Voltage
If a conductor is moved through a magnetic
field so that it cuts magnetic lines of flux, a
voltage will be induced across the conductor.
11.4 Induced Voltage
The magnitude of the induced voltage is
directly related to the speed of movement (i.e.
at which the flux is cut).
d
e
dt
Moving the conductor in parallel with the flux
lines will result in zero volt of induced voltage.
11.4 Induced Voltage
If a coil of conductor instead of a straight
conductor is used, the resultant induced
voltage will be greater
Faraday’s law of electromagnetic induction
If a coil of N turns is placed in the region of
the changing flux, as in the figure below, a
voltage will be induced across the coil as
determined by Faraday’s Law.
11.4 Induced Voltage
11.4 Induced Voltage
Changing flux also occurs in a coil carrying
a variable current.
Similar voltage will be induced, the direction
of which can be determined by Lenz’s Law.
11.4 Induced Voltage
Lenz’s law
An induced effect is always such as to
oppose the cause that produced it.
The magnitude of the induced voltage is given
by:
vL  eind
di
L
dt
d 

 L  N di 
L is known as inductance of the coil and is
measure in henries (H)
CHAPTER 12
MAGNETIC CIRCUITS
12.1 Introduction
Magnetism is an integral part of almost every
electrical device used today in industry,
research, or the home.
Generators, motors, transformers, circuit
breakers, televisions, computers, tape
recorders and telephones all employ
magnetic effects to perform a variety of
important tasks.
12.3 Reluctance
The resistance of a material to the flow of
charge (current) is determined for electric
circuits by the equation
l
l
R 
A A


1
    conductivi ty 


The reluctance of a material to the setting
up of magnetic flux lines in a material is
determined by the following equation
l

A
rels, or At/Wb 
12.4 Ohm’s Law for Magnetic Circuits
cause
effect 
opposition
For magnetic circuits, the effect is the flux .
The cause is the magnetomotive force (mmf) F,
which is the external force (or “pressure”) required
to set up the magnetic flux lines within the
magnetic material.
The opposition to the setting up of the flux  is the
reluctance .
12.4 Ohm’s Law for Magnetic Circuits
Substituting:



The magnetomotive force  is proportional
to the product of the number of turns around
the core (in which the flux is to be
established) and the current through the
turns of wire
  NI
At 
12.4 Ohm’s Law for Magnetic Circuits
An increase in the number of turns of the
current through the wire, results in an
increased “pressure” on the system to
establish the flux lines through the core.
12.5 Magnetizing Force
The magnetomotive force per unit length is
called the magnetizing force (H).

H
l
At/m 
Magnetizing force is independent of the type of
core material.
Magnetizing force is determined solely by the
number of turns, the current and the length of
the core.
12.5 Magnetizing Force
Substituting:
NI
H
l
At/m 
12.5 Magnetizing Force
The flux density and the magnetizing force are
related by the equation:
B  H
12.6 Hysteresis
Hysteresis – The lagging effect between the
flux density of a material and the magnetizing
force applied.
The curve of the flux density (B) versus the
magnetic force (H) is of particular interest to
engineers.
12.6 Hysteresis
Series magnetic circuit used to
define the hysteresis curve.
12.6 Hysteresis
The entire curve (shaded) is called the
hysteresis curve.
 The flux density B lagged behind the
magnetizing force H during the entire plotting
of the curve. When H was zero at c, B was
not zero but had only begun to decline. Long
after H had passed through zero and had
equaled to –Hd did the flux density B finally
become equal to zero
12.6 Hysteresis
Hysteresis curve.
12.6 Hysteresis
If the entire cycle is repeated, the curve obtained for
the same core will be determined by the maximum H
applied.
12.6 Hysteresis
Normal magnetization curve for
three ferromagnetic materials.
12.6 Hysteresis
Expanded view for the low magnetizing force region.
12.7 Ampere’s Circuital Law
Ampère’s circuital law: The algebraic sum
of the rises and drops of the mmf around a
closed loop of a magnetic circuit is equal to
zero; that is, the sum of the rises in mmf
equals the sum drops in mmf around a
closed loop.
  0
  

V  IR 
or
  Hl
12.7 Ampere’s Circuital Law
As an example:
  0
NI  H ablab  H bclbc  H ca lca  0
NI  H ablab  H bclbc  H calca
12.8 Flux 
The sum of the fluxes entering a junction is
equal to the sum of the fluxes leaving a
junction
12.8 Flux 
 a  b   c at juction a 
or
b   c   a at junction b
12.9 Series Magnetic Circuits :
Determining NI
Two types of problems
 is given, and the impressed mmf NI
must be computed – design of motors,
generators and transformers
NI is given, and the flux  of the magnetic
circuit must be found – design of magnetic
amplifiers
12.9 Series Magnetic Circuits :
Determining NI
Table method
A table is prepared listing in the extreme
left-hand column the various sections of
the magnetic circuit. The columns on the
right are reserved for the quantities to be
found for each section
12.9 Series Magnetic Circuits :
Determining NI
Example 12.3
Determine the secondary current I2 for the transformer if
the resultant clockwise flux in the core is 1.5 x 10-5 Wb.
12.9 Series Magnetic Circuits : Determining NI
Example 12.3 – solution
 1.5 x10 5
B 
 0.1 T
3
A 0.15 x10
12.9 Series Magnetic Circuits : Determining NI
Example 12.3 – solution (cont’d)
Based on B- H curve, is got H abcd  30
Using ampere circuital law :
N1 I1  N 2 I 2  H abcd l abcd
N 2 I 2  N1 I1  H abcd l abcd
N1 I1  H abcd l abcd
I2 
N2
60 x 2  30 x(0.16)
30
 3.84 A

At / m
12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)
Calculate Hl for each
section;
H efablefab  70  304.8 103
 21.34 At
H bcdelbcde  1600 127 10 3
 203.2 At
12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)
The magnetic circuit
equivalent
The electric circuit
analogy
NI  H efablefab  H bcdelbcde  21.34  203.2  224.54 At
224.54
I
 4.49 A
50
12.10 Air Gaps
Effects of air gaps on a magnetic circuit
The flux density of the air gap is given by;
where;
 g   core
and;
Ag  Acore
12.10 Air Gaps
Effects of air gaps on a magnetic circuit
Assuming the permeability of air is equal to that
of free space, the magnetizing force of the air
gap is determined by;
And the mmf drop across the air gap is equal to
Hg Lg;
12.10 Air Gaps
Example
A flux 0f 0.2 x 10-4 Wb will establish
sufficient
attractive
force
for
armature the armature of the relay.
a. Determine the required current to
establishd this flux level.
b. The force exert on the armature is
determined by the equation
Where Bg is the flux density within the ais gap and A is the common
area of the air gap. Find the force in newton to establish the flux.
12.10 Air Gaps
Example – solution