Part I Magnetic materials Many electrical engineering devices are based on utilising magnetic properties of materials (inductor, transformers and machines).All materials show some magnetic effect.1. Magnetic dipole moment and magnetic field1. Magnetic dipole moment and magnetic fieldConsider a current loop, the circulating current is I and theenclosed area is A, then magneticdipole moment is defined as

mm u IA=

Magnetic dipole moment in magnetic field

B =

Magnetic moment creates its own magnetic field just like a bar of magnet

Atomic magnetic momentsAn orbiting electron in an atom behaves much like a current loop therefore has a magnetic dipole moment associated with it orbital magnetic moment, orb.

The electron also has an intrinsic angular momentum, i.e. spin. The spin of the electron creates a spin magnetic moment, spin.

Magnetisation MWhen a magnetic field B0 is applied to a material, each atom responses to it, develops or acquires a net magnetic moment the material is magnetised. The extents of the magnetisation of the material is described by magnetic vector M, the material is described by magnetic vector M, defined as the magnetic dipole moment per unit volume.

=

=

N

imiV

M1

1

The magnetic field in the material now arises from the applied field B0 and a contribution from the magnetisation M

The corresponding magnetised field H is defined

MBB 0 0+=The corresponding magnetised field H is defined as

The magnetised field is also known as magnetic field intensity and is measured in A/m.

MBH =0

1

Magnetic permeabilityThe magnetic permeability at a point of P in a material is defined as

It represents to what extent a material is HB

=It represents to what extent a material is permeable by magnetic field.In practice, the relative permeability is often quoted

000

===

HB

BB

r

Magnetic susceptibilityIn practice it is often that H is known (related directly to current), the magnetisation M is related to H by the equation

HM =where is the magnetic susceptibility. Since both r and describe the magnetisation, they are related

HM =

)1( +=r

Magnetic material classificationsIn general, magnetic material are classified into four distinctive groups based on m.

Type m=r-1 ExamplesDiamagnetic negative, small Polymers, Si, CuDiamagnetic negative, small Polymers, Si, Cu

Paramagnetic positive, small Gases

Ferromagnetic positive, very large

Fe, Co, Ni

Ferrimagnetic positive, very large

Fe3O4

Magnetic DomainFerromagnetic MaterialsA magnetic domain is a region of the crystal in which all the spin magnetic moment are aligned to produce a magnetic moment in one direction only.

Formation of two domains with opposite magnetisations reduces the external field

Domain wall: the boundary between two adjacent magnetic domains (or Bloch wall).

Energy can be further reduced by closing the ends with sideway domains. The end domains are called closure domains.

A single crystal of iron does not necessarily posses a net permanent magnetisation in the absence of an applied field. This is due to the formation of magnetic domains that effectively cancel each other.When a magnetic field is applied to a crystal, magnetic dipole moments experience a torque and are gradually rotated by the applied field.Domain A enlarges and domain B shrinks.

The effect is the Bloch wall between the domain A and B migrates towards the right, resulting in a net magnetisation. This phenomenon is termed as motion of domain wall. The magnetisation process involves the motion of Bloch wall in the crystal.

Polycrystalline MaterialsThe majority of the magnetic materials used in engineering are polycrystalline. They have a microstructure that consists of many grains of various sizes and orientations.

In an unmagnetised polycrystalline sample, each crystal grain will possess domains. The domain structure in each grain will depend on the size and shape of the grain and to some extent, on the magnetisations in neighbouring grains.

Very small grains

B-H curve (Hysteresis)

Using Circuital law I

dNIHpi

=

d

S

HB r0=

Flux density is given bydpi

SB =

B depends not only on H but also on the magnetic history of the iron.

Features:Shape is symmetrical about its axes,B is not single valued function of H,B tends to lag behind H.This behaviour is known as hysteresis

When H=0, B=Br called the remanence of the iron.When B=0, H=Hc, called the coercivity.

The relative permeability of the iron

BHB r0=

HB

r =

The relative permeability ofthe iron is dependent of H

HHr 0 =

H

r

Microstructure processes of hysterisisAssume applying a very small external magnetic field (0H) along +x direction. the domain walls within various grains begin to move small distances a very small net magnetisation along the field.magnetisation along the field.

Increase the H the domain wall motions extend larger distances a larger net magnetisation.

The second step is irreversible! Why?

The walls encounter various obstacles such as crystal imperfections, impurities, second phases and so on, which tend to attract the walls hinder their motions. Take an imperfection as an example: A domain is stuck (or pinned) at an imperfection at a given field and cant move until the field intensity increases sufficiently to provide the necessary force to overcome the obstacle. Wall suddenly snaps free and shoots forward to the next Wall suddenly snaps free and shoots forward to the next obstacle.Sudden changes in lattice distortion creates lattice wave and it also induce eddy current, dissipating energy via joule heating. These processes involve energy conversion to heat and acoustic wave, which are irreversible.

As the field further increases, magnetisation continues to increase in the same format, leading to enlarge domains favourably oriented magnetisation and shrink away those with magnetisation pointing away from the applied field.Eventually, domain wall motions leave each Eventually, domain wall motions leave each crystal grain with a single domain and magnetisation in one of the easy directions.If the applied field is strong enough to align M along H, the material reaches saturation magnetisation.

If the H is gradually decreased to zero, the magnetisation in each domain will rotate to align parallel with nearest easy direction in that grain.If we apply a magnetising field in the reverse direction, -x, the magnetisation of the material, still along +x, will decrease and eventually, at a sufficient large H, M will be zero the material has been totally demagnetised.sufficient large H, M will be zero the material has been totally demagnetised.Further increase in the H will lead to the above processes but in opposite direction.

The above description is schematically shown in next overhead.

Power absorbed at t

Energy absorbed in time dt

dtdBAlHi

dtdBNAieP === 12

AlHdBdtdtdBAlHdW ==

Total energy absorbed per unit volume dt

=oB HdBW

0

Energy stored, energy returned & energy density

Let: i = current at time t H = field intensity corresponding to i at time t B = flux density corresponding to i at time t

Let an infinitely small time dt elapses so that new values become:i + di =Current at time t + dti + di =Current at time t + dtH + dH =Field intensity corresponding to i + di at time t +

dtB + dB = Flux density corresponding to i + di at time t + dt

Voltage induced in the coil

dtdBNA

dtdNe == 12

What happens when the current is brought back to zero? The material is left magnetized with a residual field OT Now the question is when the exciting current is decreasing, does

the coil absorb or return the energy back to supply. In this case dB/dt being ve, the induced voltage reverses its

polarity but direction of i remains same. In other words, current leaves from the +ve terminal of the induced voltage thereby returning power back to the supply.returning power back to the supply.

Proceeding in the same fashion as adopted forincreasing current, it can be shown that the areaPMTRP represents amount of energy returnedper unit volume. Obviously energy absorbedduring rising current from 0 to I0 is more thanthe energy returned during lowering of currentfrom I0 to 0.The balance of the energy must havebeen lost as heat in the core.

Hysteresis loop with alternating exciting current How is the operating point traced out if the exciting current is i =

Imax sin t ? The nature of the current variation in a complete cycle can be

enumerated as follows:

Let the core had no residual field when the coil is excited by i = Imax sin t

In the interval 0

Hysteresis loss & loop area

In the interval 0 t/2 i is +ve and di/dt is also +ve, moving the operating point from M to P along the path MNKP. Energy absorbed during this interval is given by the shaded area MNKPLTM (i). In the interval /2t,i is +ve but di/dt is ve, moving the operating point from P to T along the path PRT. Energy returned during

The operating point traces the perimeter of the closed area QFMNKPRTSEQ. This area is called the B-H loop of the material.

along the path PRT. Energy returned during this interval is given by the shaded area PLTRP (ii). Thus during the +ve half cycle of current variation net amount of energy absorbed is given by the shaded area MNKPRTM which is nothing but half the area of the loop (iii).

Using similar analysis, one can conclude that the total area enclosed by the B-H loop is the measure of the hysteresis loss per unit volume per cycle.

Hard and soft magnetic materials

Magnetic materials are often divided into hard & soft for their applications.

Soft magnetic materials are characterised by havingSoft magnetic materials are characterised by havingnarrow hysteresis loops, low remanence and small coercivity.

They are easily magnetised and demagnitised, are used as conductors of flux in magnetic circuits and magnetic screen

Hard magnetic materials have broad hysteresis loops, high remanence and high coercive forces. Such materials are difficult to demagnetise. They are used for making permanent magnets.The differences between the two classes can be shown in hysteresis loops.