Chapter 12

	Magnetism and Magnetic Circuits

The Nature of a Magnetic Field

	Magnetism
		Force of attraction or repulsion that acts between magnets and other magnetic materials
	Flux lines
		Show direction and intensity of this field at all points

The Nature of a Magnetic Field

	Field is strongest at poles
		Direction is from N to S
	Unlike poles attract
		Like poles repel

Ferromagnetic Materials

	Attracted by magnets
		Provide an easy path for magnetic flux
		Iron, nickel, cobalt, and their alloys
	Nonmagnetic materials such as plastic, wood, and glass
		Have no effect on the field

Electromagnetism

	Many applications of magnetism involve magnetic effects due to electric currents
	Direction of magnetic field may be determined by the Right Hand Rule

Electromagnetism

	Place your right hand around conductor with your thumb in the direction of the current
	Your fingers will point in the direction of the magnetic field
		This will always be perpendicular to the current

Flux and Flux Density

	Flux, F
		Total number of lines
	Flux density, B,
		Number of lines per unit area
		Divide total flux passing perpendicularly through an area by the area
	B = F/A

Flux and Flux Density

	Units for magnetic flux are webers (Wb)
	Area is measured in square meters
	Units for flux density
		Wb/m2 or teslas (T)
		1 tesla = 10 000 gauss
	B may also be measured in gauss
	We will work only with teslas

Magnetic Circuits

	Practical applications
		Use structures to guide and shape magnetic flux
		Called magnetic circuits
	Magnetic circuit guides flux to an air gap
		This provides field for the voice coil

Magnetic Circuits

	Playback heads on tape recorders
		VCRs and disk drives pick up the varying magnetic field and convert it to voltage

Air Gaps, Fringing, and
 Laminated Cores

	Circuits with air gaps may cause fringing
	Correction
		Increase each cross-sectional dimension of gap by the size of the gap
	Many applications use laminated cores
	Effective area is not as large as actual area

Series Elements and
Parallel Elements

	Magnetic circuits may have sections of different materials
		Cast iron, sheet steel, and an air gap
	For this circuit, flux is the same in all sections
		Circuit is a series magnetic circuit

Series Elements and
Parallel Elements

	A magnetic circuit may have elements in parallel
		Sum of fluxes entering a junction is equal to the sum leaving
	Similar to series/parallel electric circuits

Magnetic Circuits with dc Excitation

	Current through a coil creates magnetic flux
	Magnetomotive Force (MMF) Á = NI
	N is the number of turns of the coil
	Opposition of the circuit
		Reluctance  = l /µA

Magnetic Circuits with dc Excitation

	Ohm’s Law for magnetic circuits:
		f = Á/Â
	Useful analogy but not a practical solution method

Magnetic Field Intensity

	Magnetic field strength
		H, is the magnetomotive force (mmf) per unit length
	H = Á/l = NI/l
	Units are Ampere•turns/meter
	N•I = H•l

Relationship Between B and H

	B and H
		Related by the equation B = µH
			Where µ (Greek letter mu) is the permeability of the core
	Permeability
		Measure for establishing flux in a material

Relationship Between B and H

	The larger the value of µ
		The larger flux density for a given H
	H is proportional to I
		The larger the value of µ, the larger the flux density for a given circuit

Ampere’s Circuital Law

	Algebraic sum of mmfs around a closed loop in a magnetic circuit
		Zero: SÁ = 0
		Similar to KVL
		Since Á = NI, SNI = SHl
		NI - Hironliron - Hsteellsteel - Hglg= 0

Series Magnetic Circuits

	Solve a circuit where F is known
		First compute B using F/A
		Determine H for each magnetic section from B-H curves
		Compute NI using Ampere’s circuital law
		Use computed NI to determine coil current or turns as required

Series-Parallel Magnetic Circuits

	Use sum of fluxes principle and Ampere’s Law
	Find B and H for each section
	Then use Ampere’s Law

Series Magnetic Circuits

	Solve directly
		NI and required to find F, for circuits with one material
		For two or more substances
			Cannot calculate either F or H without knowing the other

Series Magnetic Circuits

	Trial and error
		Taking a guess at the flux to compute NI
		Compare this against the given NI

Forces Due to an Electromagnet

	Electromagnets
		Relays, doorbells, lifting magnets, etc.
	Force computed from flux density, the gap area, and the permeability

Properties of Magnetic Materials

	Atoms produce small, atomic-level magnetic fields
	For nonmagnetic materials, these fields are randomly arranged

Properties of Magnetic Materials

	For ferromagnetic materials
		Fields do not cancel, but instead form into domains
	If the domains in a material line up, the material is magnetized

Magnetizing a Specimen

	Current passed through it causes domains to line up
	If all fields line up, material is saturated
	If current is turned off, material will retain some residual magnetism

Magnetizing a Specimen

	Turning off current does not demagnetize the material
		Some other method must be used
	Effect is called Hysteresis

Measuring Magnetic Fields

	Hall effect
		Use when a piece of metal is placed in a magnetic fields
		Small voltage develops across it
	Fixed current
		Hall voltage is proportional to the magnetic field strength B

Measuring Magnetic Fields

	Fixed current
		Hall voltage is proportional to the magnetic field strength B.
	Direction of the field may be determined by the right-hand rule