EE220
ELECTRICAL AND
ELECTRONIC PRINCIPLES I
UNIT 6
MAGNETIC CIRCUITS
Content of Unit
5.1.
5.2.
5.3.
5.4.
5.5.
5.6.
5.7.
5. 8.
5. 9.
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Magnetic flux and flux density
Faraday’s Law
Lenz’s Law
Magnetic circuits
Magneto-motive-force (MMF)
Magnetic field Strength (H)
Permeability
Reluctance
Electric and Magnetic circuits Analogy
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Content/Objectives
1. State the properties of a magnetic flux
2. Describe the magnetic field due to current in
conductor and solenoid
3. State Faraday’s law of electromagnetic induction
and Lenz’s law
4. Describe the force on a current carrying conductor
5. Define magnetic density, magnetomotive force,
magnetic field strength, permeability, reluctance
6. Analyze magnetic circuits and its analogy with
electric circuits
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Magnetic Flux and Flux Density
• Magnetic flux Φ, measured in weber (Wb), is the amount of
magnetic field produced by a magnetic source
• Magnetic flux density is the amount of flux passing through a
defined area (A) that is perpendicular to the direction of the flux
• Magnetic flux density B =
Magnetic flux
area
=
Φ
𝐴
Shield from stray field
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Properties of Magnetic Flux
• The direction of a line of magnetic flux at any point in a non-magnetic
medium, such as air, is that of the north-seeking pole of a compass needle
placed at that point. i.e. North to South for a magnet
• Each line of magnetic flux forms a closed loop
• Lines of magnetic flux never intersect
• Lines of magnetic flux are like stretched elastic cords, always trying to
shorten themselves
• Lines of magnetic flux which are parallel and in the same direction repel one
another
• If a magnetic material, such as soft iron, is placed in the flux path, the flux
lines will pass through the soft iron rather than the surrounding air because
flux lines pass with greater ease through magnetic materials than through air.
• This principle is put to use in the shielding of sensitive electrical elements
and instruments that can be affected by stray magnetic fields
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Magnetic field due to current in a
conductor
Conductor top
View: Current entering
Single turn coil
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Screw rule
or righthand thumb
rule
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Magnetic field due to current in a
current in a solenoid (Coil)
Electromagnet
Right hand grip rule
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Faraday’s and Lenz’s laws of
Electromagnetic induction
 Faraday’s Law: an induced e.m.f. is set up whenever the
magnetic field linking that circuit changes and is
proportional to the rate of change of the magnetic flux
linking the circuit.
• 𝒆=
𝒅𝝓
𝑵
𝒅𝒕
= 𝑩𝒍𝒗𝒔𝒊𝒏θ
• where 𝑩, the flux density, 𝒍, the length of conductor in
the magnetic field, 𝒗, the conductor velocity, θ is the
angle the conductor moves to the magnetic field
 Lenz’s Law: the direction of an induced e.m.f. is always
such that it tends to set up a current opposing the motion
or the change of flux responsible for inducing that e.m.f.
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Lenz’ Law Contd’
A bar magnet passes through a coil:
(i)
(ii)
(iii)
(a) Indicate the direction of the induced I in each
case. Explain briefly.
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When magnet’s N-pole is moving into
coil,
S
N
+
I
e
(i)
Lenz’s
law
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-
induced I flows in such a direction as to
produce a N-pole
to oppose the approaching of magnet.
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When magnet reaches the middle
position of the coil,
(ii)
The induced I become zero
I is about to change direction.

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When magnet’s S-pole is leaving the coil,
N
S
-
e
+
I
(iii)
induced I flows in such a direction as to produce
a N-pole to oppose the leaving of magnet.
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Force on a current carrying
conductor
Before current flow conductor
When current flows conductor
Apply Fleming’s
Left-Hand Rule or
Motor Rule
𝐹 𝑛𝑒𝑤𝑡𝑜𝑛𝑠 ∝ (𝑓𝑙𝑢𝑥 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 × 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑐𝑢𝑟𝑟𝑒𝑛𝑡)
𝐹 = 𝐵𝑙𝐼 𝑛𝑒𝑤𝑡𝑜𝑛𝑠
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Applications of Electromagnets
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Application of Magnetic Induction
Magnetic Levitation (Maglev)
Trains
• Induced surface (“eddy”) currents that
produce field in opposite direction
 Repels magnet
 Levitates train
• Maglev trains today can travel up to 603
km/h (375 mph) in April 2015 –
covered 1.8 km in 11 seconds on a 42.8
km magnetic-levitation track
• More than twice the speed of
conventional trains (150 mph or 241
km/h)
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Magnetic circuits
Effect of air gap
Fringing
effect
Ideal airgap
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Magneto-motive-force (MMF)
• In an electric circuit, the current is due to the
existence of an electromotive force.
• By analogy, we may say that in a magnetic circuit
the magnetic flux is due to the existence of a
magnetomotive force 𝐹 (m.m.f.) caused by a
current flowing through one or more turns.
• The value of the m.m.f. is proportional to the
current 𝐼 and to the number of turns 𝑁, and is
descriptively expressed in ampereturns. mmf 𝐹 = 𝑁𝐼 amperes
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Magnetic field Strength (H)
• The magnetic field strength is the m.m.f.
gradient at any point in a field.
• If the magnetic circuit is homogeneous and of
uniform cross-sectional area, the
magnetomotive force per metre length of the
magnetic circuit is termed the magnetic field
strength.
• 𝐻=
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𝐹
𝑙
=
𝐼𝑁
𝑙
amperes per metre
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Permeability 𝝁
• Measure of the ability of a material to support the
formation of a magnetic field within itself
• The ratio B/H in a vacuum is termed the permeability
of free space and is represented by the symbol μ0
• The value of this is almost exactly the same whether the
conductor is placed in free space, in air or in any other
non-magnetic material such as water, oil, wood, copper,
etc.
𝐵
𝐻
• 𝜇0 = = 4𝜋 × 10−7 H/m for a vacuum and nonmagnetic materials
• Relative permeability 𝜇𝑟 =
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𝜇
𝜇0
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Magnetization Characteristic
(or B/H Curve)
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Reluctance 𝑆
F
Φ
• 𝑆=
• Derivation:
• Using: Φ = BA and F = Hl and
• The
F
ratio:
Φ
=
𝐻𝑙
𝐵𝐴
=
𝑙
𝜇𝑟 𝜇0 𝐴
𝐵
𝐻
= 𝜇𝑟 𝜇0
=𝑆
• Thus, 𝐹 = Φ𝑆
• The unit of reluctance is the ampere per weber,
abbreviated to A/Wb
• The reluctance of a magnetic material is proportional
to the mean length and inversely proportional to the
product of the cross sectional area and the permeability
of the magnetic material
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Magnetic Circuit Analysis
• In order to analyze any magnetic circuit, two
steps are mandatory as illustrated below:
• Step #1: Find the electric equivalent circuit that
represents the magnetic circuit.
• Step #2: Analyze the electric circuit to solve for
the magnetic circuit quantities.
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Step #1: Find the electric equivalent circuit
that represents the magnetic circuit.
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Step #2: Apply Magnetic
Kirchhoff's Laws to solve for the
unknown magnetic quantities
• First Law : Summation of fluxes entering in a
junction is equal to that of leaving
• Second Law or Amperes circuital Law :
Summation of magneto motive forces in a
closed magnetic circuit is zero
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Example: Apply Kirchhoff ’s Laws
Kirchhoff's First Law
a)
or
Amperes circuital Law
𝐹=0
b)
∴ +𝑁𝐼 − 𝐻𝑎𝑏 𝑙𝑎𝑏 − 𝐻𝑏𝑐 𝑙𝑏𝑐 − 𝐻𝑐𝑎 𝑙𝑐𝑎 = 0
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Electric and Magnetic circuits Analogy
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Tutorial 1.
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Solution
𝒍𝒄 ≫ 𝒍𝒈
Conclusion: 𝑺𝒈 ≫ 𝑺𝒄 thus, 𝑰𝒘𝒊𝒕𝒉 𝒈𝒂𝒑 ≫ 𝑰𝒏𝒐 𝒈𝒂𝒑
Explain?
Note: Draw the electric equivalent circuits
To represent the cases
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Tutorial 2
A rectangular coil measuring 200mm by 100mm is
mounted such that it can be rotated about the
midpoints of the 100mm sides. The axis of rotation is
at right angles to a magnetic field of uniform flux
density 0.05T. Calculate the flux in the coil for the
following conditions:
(a) the maximum flux through the coil and the
position at which it occurs;
(b) the flux through the coil when the 100mm sides
are inclined at 45° to the direction of the flux.
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Flux is given by:
Φ = 𝐵𝐴𝑠𝑖𝑛𝜃
Solution
a. Maximum flux
𝜃 = 90°
b. Flux at 𝜃 = 45°
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Tutorial 3.
A magnetic circuit comprises three parts in series,
each of uniform cross-sectional area (c.s.a.). They are:
(a) a length of 80mm and c.s.a. 50mm2,
(b) a length of 60mm and c.s.a. 90mm2,
(c) an airgap of length 0.5mm and c.s.a. 150mm2.
A coil of 4000 turns is wound on part (b), and the
flux density in the airgap is 0.30 T. Assuming that all
the flux passes through the given circuit, and that the
relative permeability 𝜇𝑟 is 1300, estimate the coil
current to produce such a flux density.
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Flux 𝜱:
Solution
𝑁𝑜𝑡𝑒: Φ𝑎 = Φ𝑏 = Φ𝑐
Neglecting fringing effects
(airgap: part c)
Part a. Magnetomotive force
Note: Draw magnetic
and Equiv.electric circuit:
Part a: 80 mm, 50 𝑚𝑚2
Part b: 60 mm, 90 𝑚𝑚2
Part c: 0.5mm, 150 𝑚𝑚2
N = 4000
Apply Ampere circuital Law
Part b. Magnetomotive force
Part c. Magnetomotive force
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∴ coil current to produce
a flux density of 0.3 T is:
𝐹
𝐼=
𝑁
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END OF LECTURE
“Be ready when opportunity comes... Luck is the time when preparation and
opportunity meet.”
Roy D. Chapin Jr.
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