Chapter 13
Principles of Electromechanics
Jaesung Jang
Electrostatics
B-H Magnetization Curves & Magnetic Hysteresis
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Electrostatics & Magnetic Flux
The force on a stationary charge q in an electric field E
F = qE
The force on a charge q moving at velocity u
under magnetic field with flud density B : F = q(u × B )
V = E d where E is uniformly distributed between two parallel plates,
d is the distance between two conducting plates, and
V is the potential difference between two conducting plates.
V
++++
E
d
____
Magnetic Flux Φ is defined as the number of lines of
force flowing outward from a magnet’s north pole.
Units: weber (Wb); One weber (Wb) = 1 x 108 lines
Magnetic Flux Density B is the number of lines per unit
area of a section perpendicular to the direction of flux.:
B = Φ / A (=area)
Units: Tesla (T) = 1 Wb/meter2
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Types of Magnets
• The basis of magnetic effects is the magnetic field associated with electric charges in
motion.
• Magnetic permeability is the ability to be magnetized, and it is the ability of a
material to support magnetic flux.
– Relative permeability (µr) compares a material with air. µr= µ (material) / µ (air)
• Classification of Magnetic and Nonmagnetic Materials
– Magnetic materials:
•
•
•
Ferromagnetic materials include iron, steel, nickel, cobalt, and certain alloys (usually conductors).
They can become strongly magnetized in the same direction as the external magnetizing field, with
high values of permeability.
Paramagnetic materials include aluminum, platinum, manganese, and chromium. They become
weakly magnetized in the same direction as the external magnetizing field. The permeability is
slightly more than 1.
Diamagnetic materials include copper, zinc, mercury, gold, silver, and others. They become weakly
magnetized in the opposite direction from the external magnetizing field. The permeability is slightly
less than 1.
– Nonmagnetic materials:
•
air, paper, wood, and plastics
– Ferrites are nonmetallic materials that have the ferromagnetic properties (high permeability)
of iron. Common applications include ferrite cores in the coils for RF transformers, and
ferrite beads, which concentrate the magnetic field of the wire on which they are strung.
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Field Intensity (H)
• Materials with high permeability can
produce large values of flux density B
inside the materials for an externally
applied magnetic field H.
Permeability drops drastically
at saturation.
+B
• The amount of flux produced by H depends
on the material in the field.
• These factors are reflected in this formula:
– B = µ H = µo µr H
– The unit is teslas per ampere-turn per
meter: T/((A · t)/m)
Slope of
B/H is large
-H
Saturation
+ Bmax
+H
Slope of
B/H is small
• The B-H magnetization curve shows how - Bmax
much flux density B results from increasing
-B
field intensity H.
• Saturation is the effect of little change in
Slope = Permeability
flux density when the field intensity
increases.
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Magnetic Hysteresis
• Hysteresis refers to a situation where the
magnetic flux lags the increases or decreases
in magnetizing force.
• Hysteresis loss is energy wasted in the form of
heat when alternating current reverses rapidly
and molecular dipoles lag the magnetizing force.
– For steel and other hard magnetic materials,
hysteresis losses are much higher than in soft
magnetic materials like iron.
• Hysteresis Loop
– BR is called remanent (residual) magnetization,
which is the flux density remaining after the
magnetizing force is reduced to zero.
– Note that H = 0 but BR > 0. -> permanent magnet.
– HC is the coercive force (needed to make B =
0)-> Demagnetization
•
Erasing the recorded signal on magnetic tape.
Hysteresis loop for magnetic materials. This
graph is a B-H curve like Fig. 14-3, but H
alternates in polarity with alternating current.
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Magnetic Shielding
• Shielding is to prevent one component from affecting
another through their common electric or magnetic fields.
Note: shield (방패)
• Examples of shielding:
– The braided copper wire shield around the inner conductor of
a coaxial cable.
– A shield of magnetic material enclosing a cathode-ray tube
(CRT).
• A good conductor is best for two (electrical) shielding
functions for the following applications:
– Preventing induction of static electric charges
– Shielding against the induction of a varying magnetic field.
• The best (magnetic) shield for a steady magnetic field is a
good magnetic material of high permeability. They are to
prevent external fields from interfering with the operation
of a device or instrument.
Magnetic shield
around a meter
movement.
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Motor Action between Two Magnetic
Fields
F
B
current
L
Force F = i L x B
where L is a vector pointing
in the direction of the current
Motor action of current in a straight conductor when it is in an external magnetic field. The HI is the
circular field of the current The HM indicates field lines between the north and south poles of the
external magnet.
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