Electric Machines I Introduction to Machinery
Principles
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Dr. Firas Obeidat
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Table of contents
1 • The Magnetic Field
2 • The Magnetic Circuit
3 • Faraday's and Lenz's laws
Dr. Firas Obeidat Faculty of Engineering Philadelphia University
3 Dr. Firas Obeidat Faculty of Engineering Philadelphia University
The Magnetic Field
Magnetic fields are the fundamental mechanism by which energy is converted from one form to another in motors, generators, and transformers. Four basic principles describe how magnetic fields are used in these devices
• A current-carrying wire produces a magnetic field in the area around it.
• A time-changing magnetic field induces a voltage in a coil of wire if it passes through that coil. (This is the basis of transformer action.)
• A current-carrying wire in the presence of a magnetic field has a force induced on it. (This is the basis of motor action.)
• A moving wire in the presence of a magnetic field has a voltage induced in it. (This is the basis of generator action.)
4 Dr. Firas Obeidat Faculty of Engineering Philadelphia University
The Magnetic Field
The basic law governing the production of a magnetic field by a current is
Ampere's law:
𝐻. 𝑑𝑙 = 𝐼𝑛𝑒𝑡
where H is the magnetic field intensity produced by the current Inet and dl is a
differential element of length along the path of integration. In SI units, I is
measured in amperes and H is measured in ampere-turns per meter.
If the core is composed of iron or certain
other similar metals (collectively called
ferromagnetic materials) , essentially all
the magnetic field produced by the current
will remain inside the core, so the path of
integration in Ampere's law is the mean
path length of the core lc. The current
passing within the path of integration Inet is
then Ni, since the coi1 of wire cuts the path
of integration N times while carrying
current i.
5 Dr. Firas Obeidat Faculty of Engineering Philadelphia University
The Magnetic Field
Ampere's law thus becomes
𝐻𝑙𝑐 = 𝑁𝑖
The strength of the magnetic field flux produced in the core also depends on
the material of the core.
The relationship between the magnetic field intensity H and the resulting
magnetic flux density B produced within a material is given by
𝐵 = 𝜇𝐻
H = magnetic field intensity
𝜇 = magnetic permeability of material
B = resulting magnetic flux density produced
𝜇 = 𝜇𝑜𝜇𝑟
𝜇o = 4π×10-7 H/m 𝜇r = relative permeability
Now the total flux in a given area is given by
𝜙 = 𝐵. 𝑑𝐴 =𝐵𝐴 dA: is the differential unit of area0
A: is the cross-sectional area of the core .
𝜙 =𝜇𝑁𝑖𝐴
𝑙𝑐
6 Dr. Firas Obeidat Faculty of Engineering Philadelphia University
The Magnetic Circuit
In the electric circuit, it is the voltage or electromotive force that drives the
current flow. By analogy, the corresponding quantity in the magnetic circuit is
called the magnetomotive force (mmf) . The magnetomotive force of the
magnetic circuit is equal to the effective current flow applied to the core.
𝑉 = 𝑅𝐼 𝔉 = 𝑁𝑖 𝔉 = ℜ𝜙
𝔉 = magnetomotive force of circuit
𝜙 = flux of circuit
ℜ = reluctance of circuit
V=voltage
I=current
R= resistance
ℜ =𝑙𝑐
𝜇𝐴
7 Dr. Firas Obeidat Faculty of Engineering Philadelphia University
Faraday's and Lenz's laws
Faraday's law states that if a flux passes through a turn of a coil of wire, a
voltage will be induced in the turn of wire that is directly proportional to the
rate of change in the flux with respect to time.
𝑒 =𝑑𝜙
𝑑𝑡
If a coil has N turns and if the same flux passes through all of them, then the
voltage induced across the whole coil is given by
𝑒 = 𝑁𝑑𝜙
𝑑𝑡
e= voltage induced in the coil
N=number of turns of wire in coil
ϕ=flux passing through coil
Lenz's law states that the direction
of the voltage buildup in the coil is
such that if the coil ends were short
circuited, it would produce current
that would cause a flux opposing the
original flux change.
𝑒 = −𝑁𝑑𝜙
𝑑𝑡
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