Magnetic Circuits

1
Chapter 12

• Magnetic Circuits

2
Objectives

• Demonstrate an understanding of the principles of
  magnetism and electromagnetics.
• Show how a solenoid is constructed and how it
  operates.
• Calculate the magnetic flux, magnetomotive force,
  and flux density in a closed core.
• State the relationships among reluctance,
  absolute permeability, and relative permeability.
• Explain the relationship between magnetic field
  intensity and flux density.

3
Objectives

• Read a B-H curve and find the linear and
  saturation regions on the curve.
• Explain why core saturation is generally
  detrimental to solenoid performance.

4
12-1 Magnetism and Electromagnetism
5
12-2 Flux
6
12-3 Flux Density

• B F / A
• B flux density in webers/m2 (Wb/m2) or teslas
  (T)
• F flux in webers (Wb)
• A cross-sectional area in meters2

7
12-4 Magnetomotive Force

• mmf N I
• mmf magnetomotive force in ampere-turns (A-t)
• N number of turns of wire (t)
• I coil current in amperes (A)

8
12-5 Reluctance

• F mmf / R NI / R
• F flux in webers (Wb)
• mmf magnetomotive force in ampere-turns (A-t)
• R reluctance in ampere-turns/weber (A-t/Wb)

9
12-6 Determining Magnetic Field Direction of an
Electromagnet
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12-7 Closed (Circular) Coils
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12-8 Magnetic Field Intensity

• H mmf / l NI / l
• H magnetic field intensity in
  ampere-turns/meter (A-t/m)
• mmf magnetomotive force in ampere-turns (A-t)
• l mean length of core in meters (m)
• N number of turns on the coil
• I coil current in amperes (A)

12
Two closed-core inductors with (a) short mean
length, and (b) long mean length
13
12-9 Permeability

• R l / µA
• R reluctance in ampere-turns/weber (A-t/Wb)
• l mean length of the core in meters (m)
• µ permeability in webers/ampere-turns-meter
  (Wb/A-t-m)
• A cross-sectional area of the core in meters2
  (m2)

14
Permeabiity

• µ B / H
• µ permeability in webers/ampere-turns-meter
  (Wb/A-t-m)
• B flux density in webers/meters2 (Wb/m2) or
  teslas (T)
• H magnetic field intensity in
  ampere-turns/meter (A-t/m)

15
Permeability

• µr µ / µ0
• µr relative permeability (dimensionless)
• µ absolute permeability in webers/ampere-turns-m
  eter (Wb/A-t-m)
• µ0 permeability of free-space, 4p x 10-7
  Wb/A-t-m

16
Saturation curves for steel.
17
Bipolar saturation curve.
18
B-H relationship with sinusoidal excitation.
19
B-H relationship with core saturation.