Transcript Lecture Magnetic Circuitx

Magnetic and
Electromagnetic
DR. MOHD IRFAN HATIM MOHAMED DZAHIR
What you should know at the end of
this chapter
Magnetic field
Magnetic Flux
Flux Density
Permeability
Different magnetic
materials
Reluctance
Ohms Law for
Magnetic Circuits
Magnetizing Force
Hysteresis
Ampere’s Circuital
Law
Airgap
Faradays Law
Lenz’s Law
Application of magnetic effects
Speaker
•The shape of pulsating waveform of the input current is
determined by the sound to be reproduced by the speaker.
•The higher the pitch of the sound pattern, the higher the
oscillating frequency between the peaks and valleys
resulting higher frequency of the vibration of the cone.
Coaxial High-Fidelity Loudspeaker
(b) Basic operation
(a) Overall view
(a) Cross-sectional view
Hall Effect Sensor
(a) Orientation of controlling
(b) Effect on electron flow
•Hall effect sensor is a semiconductor device that generates an
output voltage when exposed to the magnetic field.
•The difference in potential is due to separation of charge
established by the Lorentz force.
•The direction of force can be determined by left-hand rule.
Bicycle Speed Indicator
Use as sensor for alarm systems
Magnetic Field
Magnetic field
 exists in the region surrounding a permanent
magnet
 can be represented by magnetic flux lines
Magnetic flux lines (Φ)
 Representation of magnetic field.
 do not have origins or terminating points
 exist in continuous loops
 radiate from the north pole to the south pole
 returning to the north pole through the metallic bar
Magnetic Field
The strength of a magnetic field in a particular region is
directly related to the density of flux lines in that region
Magnetic field strength at point a is twice that at point b
since twice as many magnetic flux lines are associated
with the perpendicular plane at point a than at point b.
Magnetic Field
Continuous magnetic flux line will strive to occupy as
small an area as possible.
This results in magnetic flux lines of minimum length
between the unlike poles
If unlike poles of two permanent magnets
are brought together, the magnets attract
If like poles are brought together, the
magnets repel
Magnetic Field
If a nonmagnetic material, such as glass or copper, is
placed in the flux paths surrounding a permanent
magnet, an almost unnoticeable change occurs in the
flux distribution
if a magnetic material,
such as soft iron, is
placed in the flux path,
the flux lines pass
through the soft iron
rather than the
surrounding air
because flux lines
pass with greater ease
through magnetic
materials than through
air.
Magnetic Field
If a nonmagnetic material, such as glass or copper, is
placed in the flux paths surrounding a permanent
magnet, an almost unnoticeable change occurs in the
flux distribution
if a magnetic material,
such as soft iron, is
placed in the flux path,
the flux lines pass
through the soft iron
rather than the
surrounding air
because flux lines
pass with greater ease
through magnetic
materials than through
air.
Magnetic Field
The previously stated principle is used in
shielding sensitive electrical elements and
instruments that can be affected by stray
magnetic fields
Magnetic Field
A magnetic field is present around every wire
that carries an electric current
Right-hand rule can be used to determine the
direction of magnetic flux line
Magnetic Field
If the conductor is wound in a single-turn coil the
resulting flux flows in a common direction through the
center of the coil.
A coil of more than one turn produces a magnetic field
that exists in a continuous path through and around the
coil
Magnetic Field
The field strength of the coil can be effectively
increased by placing certain materials, such as
iron, steel, or cobalt, within the coil to increase
the flux density within the coil
The whole concept  electromagnetic
Magnetic Field
2 type of magnets
 Permanent magnet
• A material such as steel or iron that will remain magnetized for long periods
of time without the aid of external means.
 Electromagnet
• Magnetic effects introduce by the flow of
charge or current.
• Flux distribution is quite similar to
permanent magnet
• Have north and south pole
• Concentration of flux line is less than that
of permanent magnet
• Field strength may be increase by placing
a core made of magnetic materials (iron,
steel, cobalt)
• Parameters affecting field strength
• Currents
• Number of turn
• Material of the core
Electromagnet
Without core
With core
Magnetic Field
Right Hand Rule
 Case 1
• Thumb : Direction of
current flow
• Other fingers : Direction
of magnetic flux
 Case 2
• Thumb : Direction of
magnetic flux
• Other fingers : Direction
of current flow
Magnetic Flux
Representation of magnetic field.
Group of force lines going from the north pole
to the south pole
In the SI system of units, magnetic flux is
measured in webers (Wb) and is represented
using the symbol phi (𝚽).
8
1 Weber = 10 lines
Similar to current in electric circuit
Flux Density
The number of flux lines per unit area
Use symbol ‘B’
Measured in Tesla (T)
Magnitude of flux density
If 1 weber of magnetic flux passes through an
area of 1 square meter, the flux density is 1 tesla.
Example 1
Find the flux and the flux density in the two
magnetic cores shown in following figure. The
diagram represents the cross section of a
magnetized material. Assume that each dot
represents 100 lines or 1 µWb.
Example 1
For figure a
Flux is simply the number of lines
  49 1Wb
 49 Wb
Finding flux density
A  l  w  0.025 m  0.025 m  6.25104 m2

49 Wb
3
B 

78.4

10
T
4
2
A 6.25 10 m
Example 1
For figure b
  72 1Wb
 72 Wb
Finding flux density
A  l  w  0.025 m  0.05 m 1.25104 m2

72 Wb
3
B 

57.6

10
T
4
2
A 1.25 10 m
Note : the core with the largest flux does not necessarily have the highest flux density.
Example 2
If the flux density in a certain magnetic material
2
is 0.23 T and the area of the material is 0.38 in ,
what is the flux through the material?
Convert the area to m
A  0.38 in 2 
2
1 m2
 39.37 in 
2
1 m = 39.37 inch
 245 106 m2
  BA  0.23T  245106 m2  56.35 106Wb
Magnetomotive force
External force or 'Pressure' required to set up
the magnetic flux lines within the magnetic
material.
The cause of a magnetic field
Similar to the applied voltage in electric circuit
Measured in ampere-turns (At)
The magnetomotive force
(mmf),  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
Permeability
Definition
 the measure of the ability of a material to support
the formation of a magnetic field within itself
 degree of magnetization that a material obtains in
response to an applied magnetic field.
 Measure of the ease in which magnetic flux lines
can be established in the material
 Ability of magnetic material to conduct flux
Permeability
Permeability of air (free space)
•
Relative permeability
 The ratio of the permeability of a material to that of
free space

r 
o
Permeability
Material
Description
Example
µr
µr = 1
Nonmagnetic
materials
Permeability same
as that of free
space
copper,
aluminium, glass,
air and wood
Diamagnetic
Permeability
slightly less than
that of free space.
Bismuth, pyrolitic
carbon
µr < 1
Paramagnetic
Permeability
slightly more than
that of free space.
magnesium,
molybdenum,
lithium, and
tantalum
1 < µr < 100
Ferromagnetic
materials have a
very high level
permeability
Iron, nickel, steel
and alloys of these
materials
µr  100
Reluctance
The reluctance of a material to the setting up
of magnetic flux lines in the material
Unit : Ampere-turns / Weber
Compare this to the resistance in electric
circuit
Ohm’s Law for Magnetic Circuit
Recall
For Electric Circuit
V
I
R
Effect = Flux
For Magnetic Circuit
Cause = Magnetomotive force
Opposition = Reluctance
Example 3
Calculate the reluctance of a torus (a doughnut-shaped core) made of
low-carbon steel. The inner radius of the torus is 1.75 cm and the
outer radius of the torus is 2.25 cm. Assume the permeability of lowcarbon steel is 2X10-4 Wb/ At m
Solution:
diameter  d  a  b  0.0225 m  0.0175 m  0.005 m
0.005
radius  r 
m  0.0025 m
2
A   r 2    0.0025 2 1.96 105 m2
The length is equal to the circumference of the torus
measured at the average radius
c  b  0.0025  0.002m
a
b
c
l  2 c  2  0.02 m  0.126 m

l
0.126
6


32.1

10
At/Wb
4
5
 A 2 10 1.96 10
Example 4
Mild steel has a relative permeability of 800. Calculate
the reluctance of a mild steel core that has a length of 10
cm and has a cross section of 1.0 cm X 1.2 cm.
Solution:
  o r   4 107 Wb/At m   800   1103 Wb/At m
l  10 cm  0.10 m
A  0.010 m  0.012 m =1.2 10-4 m2
l
0.10 m
5



8.33

10
At / Wb
3
-4
2
 A 110 Wb/At m 1.2 10 m 
Magnetizing Force
Magnetomotive force per unit length
Also called magnetic field intensity
Symbol : H
Independent of the type of core material
determined solely by the number of turns, the
current, and the length of the core.
 NI
H 
l
l
 At/m 
B-H Relationship
Flux density (B) and magnetizing force are
related by the equation
B  H
However, we know that
So
B   H   r o H

r 
o
   r o
B  flux density, Wb / m 2 or T
H  magnetizing force, At/m
  permeability of the medium,Wb / At.m
o  permeability of free space,Wb / At.m
r  relative permeability
Hysterisis
Hysteresis is a characteristic of a magnetic
material whereby a change in magnetization
lags the application of the magnetic field
intensity.
The magnetic field intensity (H) can be readily
increased or decreased by varying the current
through the coil of wire, and it can be reversed
by reversing the voltage polarity across the
coil.
In other word, hysteresis is the lagging effect
between the flux density, B of a material and
the magnetizing force, H applied.
Hysterisis
Series
magnetic
circuit
used
to
define the hysteresis
curve.
Hysterisis
The entire curve (shaded) is called the
hysteresis curve.
Hysterisis
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
Hysteresis
If the entire cycle is repeated, the curve
obtained for the same core will be determined
by the maximum H applied
Normal magnetization curve for three ferromagnetic materials.
Magnetic Equivalent Circuit
Magnetic circuit
Electric circuit
Ampere’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.
Or
The sum of the rises in mmf equals the sum of
the drops in mmf around a closed loop.
  0
  
  NI  Hl
Similar to KVL in electric circuit
V  0
Ampere’s Circuital Law
  0
  NI  impressed mmf / " source "
  Hl  mmf drop / " load "
Steel
Cobalt
Iron
43
Flux 
The sum of the fluxes entering a junction is
equal to the sum of the fluxes leaving a
junction
Similar to KCL in electric circuit
 a  b   c at juction a 
b   c   a at junction b
Series Magnetic Circuit
2 types of problem:
  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
B-H curve is used
 to find H if B is given
 to find B if H is given
Example 5: Series Magnetic Circuit
Example 5: Series Magnetic Circuit
Part a: Finding I
4
  4 10 Wb
Example 5
Part a: Finding I
Use B-H curve to find H
For cast steel
When B=0.2  H=170 At/m
170
Example 5
Part a: Finding I
Use Ampere’s circuital law
NI  Hl
Hl 170 At/m    0.16 m 
3
I

 68 10 A
N
400 t
Example 5
Part b: Finding µ and µr
Example 6
1m  39.37 in
Example 6
Length of each material
Area
Example 6
Finding H for sheet steel
H  70 At/m
Example 6
Finding H for cast iron
H  1600 At/m
Example 6
Use Ampere’s circuital law
Example 7: NI is given, find flux 
Air Gaps
Fringing
 The spreading of the flux
lines outside the common
area of the core for the air
gap.
Only ideal case will be
covered in this course
Air Gaps
For ideal case
Mmf drop across the air gap
  H g lg
Permeability of air is assumed to be
equal to permeability of free space
air  o
so magnetizing force of air gap can be determined by:
Hg 
Bg
air

Bg
o

Bg
4 10
  7.96 10  Bg (At/m)
5
7
Example 8 : Air Gap
Example 8 : Air Gap
Example 8 : Air Gap
Example 9 : Air Gap
Example 9 : Air Gap
Example 9 : Air Gap
Application of magnetic effects
Faraday’s law of electromagnetic
induction
Michael Faraday discovered the principle of
electromagnetic induction in 1831.
Basically he found that moving a magnet
through a coil of wire induced a voltage across
the coil,
Two observation:
1. The amount of voltage induced in a coil is directly
proportional to the rate of change of the magnetic
field with respect to the coil (d /dt).
2. The amount of voltage induced in a coil is directly
proportional to the number of turns of wire in the
coil (N).
Faraday’s law of electromagnetic
induction
First observation
• Magnet is moved at
certain rate and certain
voltage is produced
• Magnet is moved at
faster rate and creating
a greater induced
voltage.
S
N
S
N
Faraday’s law of electromagnetic
induction
Second observation
• Magnet is moved
through a coil and
certain voltage is
produced
• Magnet is moved at
same speed through
coil that has greater
number of turn and
greater voltage is
induced
Faraday’s law of electromagnetic
induction
Faraday’s Law is stated as follows:
The voltage induced across a coil of wire equals
the number of turns in the coil times the rate of
change of the magnetic flux.
Faraday's law is expressed in equation form
as
Example 10 : Faraday’s Law
Apply Faraday's law to find the induced
voltage across a coil with 500 turns that is
located in a magnetic field that is changing at a
rate of 8000 µWb/s.
 d 
e N
   500 t  8000  Wb/s   4.0 V
 dt 
Lenz’s Law
Defines the polarity or direction of the induced
voltage.
“an induced effect is always such as to oppose
the cause that produced it.”
“When the current through a coil changes, an
induced voltage is created as a result of the
changing electromagnetic field and the polarity
of the induced voltage is such that it always
opposes the change in current.”
Lenz’s Law
• The magnetic flux linking the coil of N turns with a current I has the
distribution shown in Fig. 11.30.
• If the current through the coil increases in magnitude, the flux linking the
coil also increases.
• We just learned through Faraday’s law, however, that a coil in the vicinity of
a changing magnetic flux will have a voltage induced across it.
• The result is that a voltage is induced across the coil in Fig. 11.30 due to the
change in current through the coil.
• It is very important to note in Fig. 11.30 that the polarity of the induced
voltage across the coil is such that it opposes the increasing level of current
in the coil.