a. A magnetic fd exists in the region
surrounding a permanent
magnet/Electromagnet, which can be
represented by magnetic flux lines.
b. Magnetic flux lines do not have origins or
terminating points in continuous loops.
c. The magnetic flux lines radiate from the
north pole to the south pole, returning to the
north pole through the bar.
d. The flux lines have equal spacing within
the core and symmetric distribution outside
the magnetic material.
Magnetic Flux(F). The group of magnetic
field lines emitted outward from the north
pole of a magnet is called magnetic flux.
The symbol for magnetic flux is F(phi). The
SI unit of magnetic flux is the weber (Wb).
One weber is equal to 1 x 108 magnetic
Example: If a magnetic flux (F) has 5,000
lines, find the number of webers. F 5000
lines 1 x 108 lines/Wb 5 x 103 108 50 x
106 Wb 50 µWb
Magnetic Flux Density (B) Magnetic flux
density is the amount of magnetic flux per
unit area of a section, perpendicular to the
direction of flux. The mathematical
representation of magnetic flux density is
Magnetomotive Force(Ғ). The flux density of an
electromagnet is directly related to the number of
turns of, and current through the coil. The product
of the two called magnetomotive force, is measured
in ampere turns (At).
The magnetomotive force in an inductor is given by:
where N is the number of turns of the coil, I is the current in the
coil, Φ is the magnetic flux and
is the reluctance of the magnetic circuit.
Magnetic Permeability( μ). In electromagnetism,
permeability is the degree of magnetization of a material that
responds linearly to an applied magnetic field. Magnetic
permeability is typically represented by the Greek letter μ.
a. Diamagnetic Material. Materials that have
permeabilities slightly less than free space (μ0 =
b. Paramagnetic Material. Materials that have
permeabilities slightly greater than free space(μ0 =
c. Ferromagnetic Materials. Materials that have
permeabilities thousands time more than free space(μ0 =
4π×10−7 Wb/A.m.). Example- iron, nickel, steel, cobalt and
d. Relative Permeability. The ratio of permeability of a
material to that of the permeability of free space.
Magnetic Fd Strength(H). Magnetic fd
strength at any point within a magnetic fd is
numerically equal to the force experienced by
an N-pole of 1 weber placed at that point.
Suppose it is required to find the field
intensity at a point A distant r meters from a
pole of m webers. Than
Intensity of Magnetization (I). It may be
defined as the induced pole strength
developed per unit area of the bar. Also it is
the magnetic moment developed per unit
volume of the bar. It is the flux density
produced in a substance due to its own
Let m = pole strength induced in the bar
A = face or pole area of the bar in m3
I =m/A Wb/m2
Or I = M/V (Magnetic moment/volume)
Characteristics of Ferromagnetic Material/Theory of
a. Ferromagnetic materials exhibit a strong attraction to magnetic
fields and are able to retain their magnetic properties after the external
field has been removed.
b. Ferromagnetic materials have some unpaired electrons so their
atoms have a net magnetic moment.
c. Ferromagnetic materials get their magnetic properties not only
because their atoms carry a magnetic moment but also because the
material is made up of small regions known as magnetic domains. In
each domain, all of the atomic dipoles are coupled together in a
preferential direction. This alignment develops as the material develops
its crystalline structure during solidification from the molten state.
d. When a ferromagnetic material is in the unmagnitized state, the
domains are nearly randomly organized and the net magnetic field for
the part as a whole is zero. When a magnetizing force is applied, the
domains become aligned to produce a strong magnetic field within the
part. Iron, nickel, and cobalt are examples of ferromagnetic materials.
a. Definition. It may be defined as the lagging of
magnetization or induction flux density (B) behind
the magnetizing force (H).
b. Basic formula B = μH
(1) No applied field
(5) Polarity Reversed
(8) Loop complete.
Faraday’s Law Page 472 (Boylestad)
"An induced current is always in such a direction
as to oppose the motion or change causing it"
When an emf is generated by a change in
magnetic flux according to Faraday's Law, the
polarity of the induced emf is such that it produces
a current whose magnetic field opposes the
change which produces it. The induced magnetic
field inside any loop of wire always acts to keep
the magnetic flux in the loop constant. In the
examples below, if the B field is increasing, the
induced field acts in opposition to it. If it is
decreasing, the induced field acts in the direction
of the applied field to try to keep it constant.
Hysteresis loss is a heat loss caused by the magnetic
properties of the armature. When an armature core is in
a magnetic field, the magnetic particles of the core tend
to line up with the magnetic field. When the armature
core is rotating, its magnetic field keeps changing
direction. The continuous movement of the magnetic
particles, as they try to align themselves with the
magnetic field, produces molecular friction. This, in turn,
produces heat. This heat is transmitted to the armature
windings. The heat causes armature resistances to
To compensate for hysteresis losses, heat-treated silicon
steel laminations are used in most dc generator
armatures. After the steel has been formed to the proper
shape, the laminations are heated and allowed to cool.
This annealing process reduces the hysteresis loss to a
An eddy current (also known as Foucault current) is an
electrical phenomenon discovered by French physicist
Léon Foucault in 1851. It is caused when a conductor is
exposed to a changing magnetic field due to relative motion of
the field source and conductor; or due to variations of the field
with time. This can cause a circulating flow of electrons, or a
current, within the body of the conductor. These circulating
eddies of current create induced magnetic fields that oppose
the change of the original magnetic field due to Lenz's law,
causing repulsive or drag forces between the conductor and
the magnet. The stronger the applied magnetic field, or the
greater the electrical conductivity of the conductor, or the faster
the field that the conductor is exposed to changes, then the
greater the currents that are developed and the greater the
Eddy Current loss
The core of a generator armature is made from soft iron, which is a
conducting material with desirable magnetic characteristics. Any
conductor will have currents induced in it when it is rotated in a
magnetic field. These currents that are induced in the generator
armature core are called EDDY CURRENTS. The power dissipated
in the form of heat, as a result of the eddy currents, is considered a
Core loss (or iron loss) is a form of energy loss that occurs in
electrical transformers and other inductors. The loss is due to a
variety of mechanisms related to the fluctuating magnetic field,
such as eddy currents and hysteresis. Most of the energy is
released as heat, although some may appear as sound ("hum").
Core losses do not include the losses due to resistance in the
conductors of the windings, which is often termed "copper loss".