EET141 Electric Circuit II MAGNETIC CIRCUIT -Part 2- CHAPTER 5 MAGNETIC CIRCUIT -Part 2-

MAGNETISM Since ancient times, certain materials, called magnets, have been known to have the property of attracting tiny pieces of metal. This attractive property is called magnetism. N S Bar Magnet N S

MAGNETIC POLES S N Iron filings The strength of a magnet is concentrated at the ends, called north and south “poles”. N S E W Compass Bar magnet

MAGNETIC ATTRACTION-REPULSION Magnetic Forces: Like Poles Repel Unlike Poles Attract

Flux distribution for a permanent magnet. MAGNETIC FIELD Flux distribution for a permanent magnet.

Flux distribution for two adjacent, opposite poles. MAGNETIC FIELD Flux distribution for two adjacent, opposite poles.

MAGNETIC FLUX Magnetic flux is the amount of magnetic field (or the number of lines of force) produced by a magnetic source. Symbol: Φ (phi) Unit: Weber (Wb)

MAGNETIC FLUX DENSITY Magnetic flux density is the amount of flux passing through a defined area that is perpendicular to the direction of the flux. Symbol: B Unit: Tesla (T)

MAGNETIC FLUX DENSITY Where B = Magnetic Flux Density (T) Φ = Magnetic Field/Flux (Wb) A = Cross sectional area (m2)

EXAMPLE 1 For the core of figure below, determine the flux density, B in teslas.

EXAMPLE 2 A magnetic pole face has a rectangular section having dimensions 200 mm by 100 mm. If the total flux emerging from the pole is 150 μWb, calculate the flux density.

SOLUTION

EXAMPLE 3 The maximum working flux density of a lifting electromagnet is 1.8 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 353 mWb, determine the radius of the pole face.

SOLUTION

MAGNETOMOTIVE FORCE Magnetomotive force (mmf) is proportional to the product of the number of turns around the core (in which the flux is to be established) and the current through the turns of wire. Symbol: F Unit: Ampere-Turn (At)

MAGNETOMOTIVE FORCE Where F = Magnetomotive Force (At) N = Number of turns (t) I = Current (A)

PERMEABILITY The level of magnetic flux established in a ferromagnetic core is a direction function of the permeability of the material. Ferromagnetic materials have very high level of permeability while non magnetic materials such as air and wood have very low levels.

PERMEABILITY The ratio of the permeability of a material to that of free space is called its relative permeability; that is, μr = relative permeability μ = permeability of the material (H/m) μ0 = 4π x 10-7 (H/m)

RELATIVE PERMEABILITY

RELUCTANCE Reluctance is the ‘magnetic resistance’ of a magnetic circuit to the presence of magnetic flux. Symbol: R Unit: At / Wb

RELUCTANCE R = the reluctance (At / Wb) l = the length of the magnetic path (m) A = the cross-sectional area (m2) μ = permeability of the material (H/m)

OHM’S LAW FOR MAGNETIC CIRCUITS For magnetic circuits, the effect desired is the flux. The cause is the magnetomotive force (mmf) , which is the external force (or “pressure”) required to set up the magnetic flux lines within the magnetic material. The opposition to the setting up of the flux is the reluctance.

EXAMPLE 4 Determine the reluctance of a piece of mumetal of length 150 mm and cross-sectional area 1800 mm2 when the relative permeability is 4000. Find also the permeability of the mumetal.

SOLUTION

EXAMPLE 5 A mild steel ring has a radius of 50 mm and a cross-sectional area of 400 mm2. A current of 0.5 A flows in a coil wound uniformly around the ring and the flux produced is 0.1 mWb. If the relative permeability at this value of current is 200 find: the reluctance of the mild steel the number of turns on the coil

SOLUTION

SOLUTION b)

MAGNETIZING FORCE Magnetizing Force or Magnetic Field Intensity is the magnetomotive force per unit length. Symbol: H Unit: At/m

MAGNETIZING FORCE The direction of the flux can be determined by placing the fingers of the right hand in the direction of current around the core and noting the direction of the thumb.

MAGNETIZING FORCE It is interesting to realize that the magnetizing force is independent of the type of core material It is determined solely by the number of turns, the current, and the length of the core.

EXAMPLE 6 A magnetizing force of 8000 At/m is applied to a circular magnetic circuit of mean diameter 30 cm by passing a current through a coil wound on the circuit. If the coil is uniformly wound around the circuit and has 750 turns, find the current in the coil.

SOLUTION

Relation between Flux Density & Magnetizing Force The flux density and the magnetizing force are related by the following equation:

B-H CURVE A curve of the flux density B versus the magnetizing force H of a material is of particular importance to the engineer. Curves of this type can usually be found in manuals, descriptive pamphlets, and brochures published by manufacturers of magnetic materials.

B-H / HYSTERESIS CURVE A typical B-H curve for a ferromagnetic material such as steel can be derived using the setup of figure below

B-H / HYSTERESIS CURVE

B-H / HYSTERESIS CURVE

Parallel Quantities in Electric and Magnetic Circuit Electric Quantities Magnetic Quantities Current, I Magnetic flux, Ф Current density, J Magnetic flux density, B Conductivity, ơ Permeability, μ Electromotive force, E Magnetomotive force, F Resistance, R Reluctance, R

Ampere’s Circuital Law Ampere’s Circuital Law states that the algebraic sum of the rises and drops of the mmf around a closed loop of a magnetic circuit is equal to zero; that is, the sum of the rises in mmf equals the sum of the drops in mmf around a closed loop.

MAGNETOMOTIVE FORCE

Ampere’s Circuital Law

Ampere’s Circuital Law

Ampere’s Circuital Law

THE FLUX Φ If we continue to apply the relationships described in the previous section to Kirchhoff’s current law, we will find that the sum of the fluxes entering a junction is equal to the sum of the fluxes leaving a junction; that is, for the circuit of Figure below.

THE FLUX Φ

EXAMPLE 7 For the series magnetic circuit of figure below: a. Find the value of I required to develop a magnetic flux of 4 x 10-4 Wb. b. Determine μ and μr for the material under these conditions.

SOLUTION

SOLUTION a) Using BH Curve

SOLUTION b)

EXAMPLE 8 Determine the secondary current I2 for the transformer of figure below if the resultant clockwise flux in the core is 1.5 x 10-5 Wb.

SOLUTION

SOLUTION

AIR GAPS In electric machines, the rotor is physically isolated from the stator by the air gap. Practically the same flux is present in the poles (made by magnetic core) and the air gap. To maintain the same flux density, the air gap will require much more mmf than the core.

AIR GAPS The spreading of the flux lines outside the common area of the core for the air gap in figure below

AIR GAPS

FRINGING EFFECT Fringing Effect: Bulging of the flux lines in the air gap. Effect: The effective cross section area of air gap increase so the reluctance of the air gap decrease. The flux density Bg < Bc (Bc is the flux density in the core). If the air gaps is small, the fringing effect can be neglected.

FRINGING EFFECT If the air gaps is small, the fringing effect can be neglected. In practical, large air gap will be divided into several small air gaps to reduce the fringing effect.

EXAMPLE 9 Find the value of I required to establish a magnetic flux of 0.75 x 10-4 Wb in the series magnetic circuit of Figure below.

SOLUTION

SOLUTION