ELET 4143 Electrical Machines and
Controls
Electromagnetism (Cont.)
Chap 2 Wildi
Spring 2008
Magnetic Flux
The group of magnetic field lines emitted outward from
the north pole of a magnet is called magnetic flux, φ.
The SI unit of magnetic flux is the weber (Wb).
One weber is equal to 1 x 108 magnetic field lines.
Example: If a magnetic flux (φ) has 5,000 lines, find the
number of webers.
φ = 5000/(1x108) = 50 x 106 Wb = 50 μWb
Magnetic Flux Density
Magnetic flux density is the amount of magnetic flux per unit
area of a section, perpendicular to the direction of flux.
Β=φ/Α
where
B = magnetic flux density, [Teslas]
φ = magnetic flux [Wb]
A = Area of the section with magnetic lines [m2]
Tesla = Weber / m2
Magnetic fields exert a force on any charge in motion.
If a wire with a current is placed in a magnetic filed B, as
shown below, then a force will move the wire upwards.
The direction of the force can be
found as:
• Take your right hand and point
your thumb toward the direction
of current.
• Then take your four other
fingers and point them in the
direction of the B field.
• The force should come up out
of your palm.
Fields Around Currents
When current flows through a wire, a
magnetic field would be generated
because the moving charges.
For a straight conductor, the magnetic
field always circles around the crosssection of the wire
The direction of the B field can be found as:
• Use your right hand and point your thumb in the direction
of the positive current flow.
• Next, take your four other fingers and curl them around.
• The circle that those fingers make is the direction of the B
field around the wire.
A solenoid is a wire that has been coiled up.
The magnetic field of a solenoid resembles that of a bar magnet.
The lines of flux come out of the north pole at one end and curve around
back to the south pole.
Placing a piece of iron or another ferromagnetic material inside the coil, it will
become an electromagnet.
The strength of the field increases as the number of coils increase.
To determine the direction of the north pole:
• Using your right hand, take your four fingers
and curl them around in the direction of positive
charge current around the coils.
• Stick your thumb out and that should be the
direction of the B field inside the solenoid and
also the direction of the north pole.
Voltage Induced in a Conductor
In many motors and generators, the coils move with respect
to a flux that is fixed in space.
The relative motion produces a change in the flux in the coils
and a voltage is induced according to Faraday’s Law.
The voltage induced is given by:
E=Blv
E = induced voltage (volts)
B = Magnetic Flux density (T)
l = Active length of the conductor in the magnetic field (m)
v = Relative speed of the conductor (m/s)
ƒ The amount of induced voltage depends on the
number of flux lines cut by the conductor, and the rate at
which the conductor cuts the line of flux.
ƒ The greater the lines of flux, the greater the induced
voltage and current.
ƒ The most voltage induced in a conductor occurs when
the conductor cuts through the magnetic flux at a 90o
angle.
ƒ The least amount voltage is produced when the
conductor moves parallel to the line of flux.
ƒ Also, the faster the conductor cuts through the lines of
flux, the greater the induced voltage will be.
ƒ The induced voltage can also be increased by coiling
the conductor that cuts the magnetic flux.
ƒ The more turns that pass through the magnetic field, the
greater the induced voltage will be.
ƒ This is because the voltage produced in each conductor
of the coil produces a voltage that adds together to a total
induced voltage.
Lorentz force on a conductor
When a current-carrying conductor is placed in a
magnetic field, it is subject to a force called
electromagnetic force or Lorentz Force
The magnitude of the force depends on the
orientation of the conductor with respect to the
direction of the field
ƒ The force is greatest when the conductor is
perpendicular to the magnetic field.
ƒ The force is zero when the conductor is parallel to
the magnetic field.
Residual Flux Density and
Hysteresis Loop
Residual Flux Density
Consider a coil around a ferromagnetic material ring.
A current source produces a current I
As I increases, so that H and B increase (curve oa)
As we reach Imax, then the magnetic field reaches a
value Bm for a magnetic filed strength Hm
• If the current in now gradually reduced to zero, the
magnetic field B, does not follow the original curve.
• Instead, it will follow the curve ab
Note that as H is reduced to zero, a substantial
magnetic flux density B remains
H = 0 ; B = Br (residual induction)
• To eliminate the residual induction, a reverse current
– I has to be applied to the coil.
• As we do so, we move along the curve bc
• The magnetic domain gradually
changes their previous orientation
until the magnetic flux density B
becomes zero at point c
• The magnetic field strength
H required to reduce the
magnetic flux to zero (B =0) is
called coercive force Hc
Nota that in order to reduce Br to zero, energy needs
to be applied to the to the material. This energy is
dissipated as heat in the material.
Hysteresis Loop
• Transformers and most electric motors operate on
alternate current (AC).
• In such devices the magnetic flux, B, in the iron changes
continuously in value and in direction.
• The peak magnetic flux
density alternates between
+Bm and – Bm, and the
magnetic field strength
alternates between +Hm and
– Hm
ƒ In the hysteresis loop, the magnetic flux moves :
+Bm, +Br, 0, –Bm, – Br, 0, +Br …
ƒ The magnetic material absorbs energy each cycle, and
dissipates energy as heat.
ƒ The area under the
hysteresis loop represents
the heat released per cycle
(60 cycles in a 60 Hz signal)
ƒ To reduce hysteresis losses,
magnetic materials that have a
narrow hysteresis loop, such
as the grain-oriented silicon
steel, are used in the cores of
AC transformers.
Eddy Currents
ƒ Consider a AC flux, φ, that links a rectangular-shaped
conductor.
ƒ According to Faraday’s law, an AC voltage E1 is
induced across its terminals.
ƒ If the conductor is shorted circuited, and AC current I1
will appear.
If a second conductor is placed inside the first, a smaller
voltage, E2, is induced because it links a smaller flux.
If we keep adding conductors inside each one, we can have
a densely packed set of rectangular conductors. This will be
equivalent to have a solid metal plate where a AC flux
passes through it.
Currents will swirl back
and forth inside the plate
(Eddy Currents)
Eddy currents can be very large
due to the low resistance of the
plate
Therefore, a metal plate
that is exposed to an AC
flux can become very hot.
ƒ The Eddy currents problem becomes important
when iron has to carry an AC flux. And this is the case
in all AC motors and transformers
ƒ A large core could become red hot, even at 60 Hz,
due to the Eddy current losses.
ƒ To reduce the losses, the core can be splitted in thin
laminations.
The Eddy currents produce large
I2R losses which are converted
into heat.
The power loss is proportional to
the square of the speed and the
square of the flux density.
a) Voltage induced in a revolving armature
b) Large Eddy currents
a) Armature built up of thin laminations
b) Much smaller Eddy currents are induced