CONTENT
 Introduction
 Magnetizing force, Intensity, MMF, Flux and their relations
 Permeability, Reluctance and Permeance
 Analogy between Electric and Magnetic circuits
 B – H Curve
 Hysteresis loop
 Series & Parallel magnetic circuit

ON
 Electromagnet: When current flows through a coil (with
or without core material), it produces a magnetic field.
 Faraday’s laws of electromagnetic induction: When ever
a conductor links with a magnetic field changes, an emf
is induced in it.
 Its magnitude is given by,
 The direction of the induced emf is given by Lenz’s law.

FORCE
It is a measure of the influence of a magnet in the surrounding
space, also known as magnetic field strength. It is denoted by H
and is given by,
Where N = No. of turns in the coil
I = Current flowing through the coil
L = Length of the coil
𝐻=
𝑁𝐼
𝐿

&MAGNETO-MOTIVE FORCE
(MMF)


FLUX & FLUX DENSITY
In the region surrounding a permanent magnet there exists a
magnetic field, which can be represented by magnetic flux
lines.
The symbol for magnetic flux is the Greek letter φ. Its unit is
Weber (Wb).
The number of flux lines per unit area is called the flux
density, is denoted by the capital letter B, and is measured in
tesla (T) or .

PERMEABILITY
The permeability (μ) of a material, is a measure of the
ease with which magnetic flux lines can be established
in the material.
Materials in which flux lines can readily be set up are
said to be magnetic and to have high permeability.
The permeability of free space (vacuum) is
The ratio of the permeability of a material to that of
free space is called its relative permeability; that is,
or

RELUCTANCE
Reluctance is the property of a material which opposes
the flow of flux within it.
It is given by the ratio of mmf to flux, i.e.
Also
Where A = Area of cross section of the magnetic path.
Length of the magnetic path
Its unit is AT/Wb.

Permeance
It is the measure of the ease with which flux can be set
up in a material. In other words, it measures the
magnitude of the flux for the number of turns in an
electric circuit.
The permeance of the magnetic circuit is expressed as:

Analogy between Electric and
Magnetic circuits
Electrical circuit Magnetic circuit
Voltage v
Current I
Resistance R
Conductivity 1/ρ
Current density J
Electric field E
Magnetomotive force F = NI
Magnetic flux φ
Reluctance R
Permeability µ
Magnetic flux density B
Magnetic field intensity H

B – H CURVE
When current is increased through the coil its mmf (NI)
increases which increases the magnetic field intensity (H).
Hence magnetic flux density increases which is proportional to
the magnetic field intensity.
Increase in flux density primarily depends on the degree of
orientation.
If a graph is plotted H vs. B, the graph is known as B-H curve.

B – H curve for different material is shown below.
B – H Curve

HYSTERESIS LOOP
The loop formed in one complete cycle of magnetization and
demagnetization is known as hysteresis loop.
The area of the hysteresis loop gives the hysteresis loss
occurred in a magnetic material due to reversal of magnetic
field.

LOOP
 The flux density remained when current is made zero is
known as residual magnetism (a – c & a – f)).
 This field intensity which forced the magnetic flux to be
zero is known as coercive force (a – d & a – g)).
 The property of the material due to which some magnetic
flux density is retained after the field intensity becomes
zero is known as retentivity.
 The area of the hysteresis loop gives the hysteresis loss
occurred in the material due to reversal of magnetic field
through it.

SERIES MAGNETIC CIRCUIT
The Series Magnetic Circuit is defined as the magnetic
circuit having a number of parts of different
dimensions and materials carrying the same magnetic
field.
Series magnetic circuit with its electrical equivalent circuit

CIRCUIT
Series circuit involving two mediums, namely (i) iron and (ii)
air.
Let,
 Number of turns = N
 Exciting current in A
 Mean length of the flux path through iron = in m
 Length of the flux path through air = in m
 Cross sectional area of the magnetic path = A in
Magnetic field strength required for iron path,
Magnetic field strength required for air gap,

CIRCUIT
Total mmf,
So when two reluctances are connected in series having
different reluctance segments, total reluctance will be the sum
of individual reluctances.

Series magnetic circuit
Example:
A closed magnetic circuit of cast steel contains a 6 cm long
path of cross-sectional area 1 and a 2 cm path of cross-
sectional area 0.5 . A coil of 200 turns is wound around the 6
cm length of the circuit and a current of 0.4 A flows.
Determine the flux density in the 2 cm path, if the relative
permeability of the cast steel is 750.
Solution:
 For the 6 cm long path:
Reluctance,

SERIES MAGNETIC CIRCUIT
 For the 2 cm long path:
Reluctance,
 Total circuit reluctance,
 Flux density in the 2 cm path,

CIRCUIT
 A magnetic circuit having two or more than two paths for
the magnetic flux is called a parallel magnetic circuit.
 The parallel magnetic circuit contains different dimensional
areas and materials having various numbers of paths.
 Parallel magnetic circuit with its electrical equivalent circuit

CIRCUIT
Example:
In the magnetic circuit detailed in Figure with all dimensions in mm,
calculate the required current to be passed in the coil having 200 turns in
order to establish a flux of 1.28 mWb in the air gap. Neglect fringing
effect and leakage flux. The B-H curve of the material is given in Figure
below. Permeability of air may be taken as, .

Parallel magnetic circuit
The path CFED is in fact path 1 where flux will remain same.
Similarly the path DC (path 2) will carry same flux and path
CBAD (path 3) will carry same flux .
 Calculation of mmf required for the path 2:
Cross sectional area of central limb,

Flux density,
mmf required for gap
Calculation for the mmf required in the iron portion of the
central limb:
Flux density,
Corresponding H from graph,
Mean iron length,
mmf required for iron portion

CIRCUIT
Total mmf required for iron & air gap (central limb),
Due to parallel connection, mmf acting across path 1 is same as mmf
acting across path 2.
Mean length of the path DEFC,
Corresponding flux density from graph,
Area of cross section of path DEFC,
Flux passing through DEFC,
Flux in path CBAD,

Area of cross section of path CBAD,
Flux density in path CBAD,
Corresponding H from graph,
Mean length of path CBAD,
Total mmf required for path CBAD
mmf to be supplied by the coil,

electric and magnetic circuit in Circuit and network theory

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