2. The Nature of a Magnetic Field
• Magnetic field
– Force field
• Magnetic flux
– Flux lines (lines of
force)
• Show direction and
intensity of the field
3. The Nature of a Magnetic Field
(cont’d.)
• Unlike poles attract
• Like poles repel
4. Ferromagnetic Materials
• Magnetic materials
– Materials attracted by
magnets
– Iron, nickel, cobalt, and
their alloys
– Provide an easy path for
magnetic flux
7. Electromagnetism
• Right hand rule for a uniform length
conductor
– Used to indicate field direction
– Place right hand around conductor
– Thumb points in direction of current
– Fingers point in direction of the field
8.
9. Electromagnetism (cont’d.)
• Rule for coils
– Curl fingers of right hand around coil in
direction of the current
– Thumb will point in direction of the field
10.
11. Magnetic Flux and Flux Density
• Weber
– Unit of flux
• Tesla
– Unit of flux density
1 𝑇 =
1 đť‘Šđť‘Ź
đť‘š2
Equation 12-1
12. Magnetic Flux and Flux Density
(cont’d.)
• Example:
• For the magnetic core
shown, the flux density at
cross section 1 is B1 = 0.4T
• Determine B2
14. Magnetic Circuits
• Found in motors, generators, speakers,
transformers
• Magnetic fields can be created by electric
currents
– Or electric currents and permanent magnets
• Example: speaker application in Figure 12-4
16. Magnetic Circuits (cont’d.)
• Magnetic stripe containing information
– Used in bank ATM cards, library cards, etc.
– Magnetic patterns encode information
– Reader sees varying magnetic field
• Induces a voltage in the pickup winding
• Voltage is amplified and sent to decoding circuitry
• MRI machine uses superconductor coils
– Create intense magnetic field
18. Air Gaps, Fringing, and
Laminated Cores
• Most practical magnetic circuits:
– Have air gaps essential to their operation
• Fringing occurs at air gaps
19. • Fringing occurs at air gaps
– Results in slight weakening of the field in the
gap
• In a gapped inductor, airgap fringing flux induces
eddy currents in coil conductors in the vicinity of
the airgap, producing unwanted power loss and
heat in the coil.
• Can be neglected for short gaps
• Or estimate the effect by increasing each cross-
sectional dimension of the core by gap length
20. Air Gaps, Fringing, and
Laminated Cores (cont’d.)
• Lamination
– Core is created with thin sheets of stacked
iron or steel
• Stacking factor
– Ratio of actual area of ferrous material to
physical area of the core
– Use to determine core’s effective area
23. Magnetic Circuits with DC
Excitation
• Two basic problems
– Determine current required to produce a given
flux
– Compute flux produced by a given current
24. MMF: The Source
of Magnetic Flux
• Current through a coil creates magnetic
flux
– The greater the current or number of turns,
the greater the flux
• Magnetomotive force (mmf)
– Measured in ampere-turns
– Denoted by the symbol
25. MMF: The Source
of Magnetic Flux (cont’d.)
• Equation defining mmf
Equation 12-2
26. Reluctance : Opposition to
Magnetic Flux
• Opposition that circuit presents to flux
Where µ=material permeability
Equation 12-3
27. Reluctance : Opposition to
Magnetic Flux (cont’d.)
• Permeability measures ease of
establishing magnetic flux in a material
– Ferromagnetic materials have high
permeability
– Nonmagnetic materials have low permeability
28. Ohm’s Law for Magnetic Circuits
• Flux does not flow like current
Equation 12-4
29. Magnetic Field Intensity and
Magnetization Curves
• Magnetic field intensity, H
– Also called magnetizing force
– Measures mmf per unit length of a circuit
Equation 12-5
Equation 12-6
30. Magnetic Field Intensity and
Magnetization Curves (cont’d.)
• Electric circuit analogy
– NI is an mmf source
– Hl is an mmf drop
33. Force Due to an Electromagnet
• Electromagnets
– Used in relays, doorbells, lifting magnets
• Where Bg is the flux density in the gap in teslas
Ag is gap area in square meters
F is force in Newtons
Equation 12-13
39. Measuring Magnetic Fields
• Hall effect
– The Hall effect is the production of a voltage
difference (the Hall voltage) across an
electrical conductor when the current flows
through the conductor in a magnetic field.
41. Transformer
• A transformer is a device that changes ac electric power at
one voltage level to ac electric power at another voltage
level through the action of a magnetic field.
• There are two or more stationary electric circuits that are
coupled magnetically.
• It involves interchange of electric energy between two or
more electric systems
• Transformers provide much needed capability of changing
the voltage and current levels easily.
– They are used to step-up generator voltage to an appropriate
voltage level for power transfer.
– Stepping down the transmission voltage at various levels for
distribution and power utilization.
42. Transformer Classification
• In terms of number of windings
– Conventional transformer: two windings
– Autotransformer: one winding
– Others: more than two windings
• In terms of number of phases
– Single-phase transformer
– Three-phase transformer
• Depending on the voltage level at which the winding is operated
– Step-up transformer: primary winding is a low voltage (LV)
winding
– Step-down transformer : primary winding is a high voltage (HV)
winding
43. Primary and Secondary Windings
A two-winding transformer consists of two windings interlinked
by a mutual magnetic field.
– Primary winding – energized by connecting it to an input
source
– Secondary winding – winding to which an electrical load is
connected and from which output energy is drawn.
Primary winding Secondary winding
44. Ideal Transformers
• No iron and copper losses
• No leakage fluxes
• A core of infinite magnetic permeability and of infinite
electrical resistivity
• Flux is confined to the core and winding resistances are
negligible
An ideal transformer is a lossless device with an input winding
and an output winding. It has the following properties: