Friday, February 8, 2013

Electronics Tutorial about Magnetism


Electromagnetism is produced when an electrical current flows through a simple conductor such as a piece of wire or cable. A small magnetic field is created around the conductor with the direction of this magnetic field with regards to its "North" and "South" poles being determined by the direction of the current flowing through the conductor.
Magnetism plays an important role in Electrical and Electronic Engineering because without it components such as relays, solenoids, inductors, chokes, coils, loudspeakers, motors, generators, transformers, and electricity meters etc, would not work if magnetism did not exist.
Then every coil of wire uses the effect of electromagnetism when an electrical current flows through it. But before we can look at Magnetism and especially Electromagnetism in more detail we need to remember back to our physics classes of how magnets and magnetism works.

The Nature of Magnetism

Magnets can be found in a natural state in the form of a magnetic ore, with the two main types being Magnetite also called "iron oxide", ( FE3O4 ) and Lodestone, also called "leading stone". If these two natural magnets are suspended from a piece of string, they will take up a position inline with the earths magnetic field always pointing north. A good example of this effect is the needle of a compass. For most practical applications these natural occurring magnets can be disregarded as their magnetism is very low and because nowadays, man-made artificial magnets can be produced in many different shapes, sizes and magnetic strengths.
There are basically two forms of magnetism, "Permanent Magnets" and "Temporary Magnets", with the type being used dependant upon its application. There are many different types of materials available to make magnets such as iron, nickel, nickel alloys, chromium and cobalt and in their natural state some of these elements such as nickel and cobalt show very poor magnetic quantities on their own. However, when mixed or "alloyed" together with other materials such as iron or aluminium peroxide they become very strong magnets producing unusual names such as "alcomax", "hycomax", "alni" and "alnico".
Magnetic material in the non-magnetic state has its molecular structure in the form of loose magnetic chains or individual tiny magnets loosely arranged in a random pattern. The overall effect of this type of arrangement results in zero or very weak magnetism as this haphazard arrangement of each molecular magnet tends to neutralise its neighbour.
When the material is Magnetised this random arrangement of the molecules changes and the tiny unaligned and random molecular magnets become "lined-up" in such a way that they produce a series magnetic arrangement. This idea of the molecular alignment of ferromagnetic materials is known as Weber's Theory and is illustrated below.

Magnetic Molecule Alignment of a Piece of Iron and a Magnet

Loose and Ordered Magnetic Molecules

Weber's theory is based on the fact that all atoms have magnetic properties due to the spinning action of the atoms electrons. Groups of atoms join together so that their magnetic fields are all rotating in the same direction. Magnetic materials are composed of groups of tiny magnets at a molecular level around the atoms, and a magnetised material will have most of its tiny magnets lined up in one direction only to produce a north pole in one direction and a south pole in the other direction.
Likewise, a material that has its tiny molecular magnets pointing in all directions will have its molecular magnets neutralised by its neighbouring magnet, thereby neutralising any magnetic effect. These areas of molecular magnets are called "domains".
Any magnetic material will produce a magnetic field itself which depends on the degree of alignment of magnetic domains in the material set up by orbital and spinning electrons. This degree of alignment can be specified by a quantity known as magnetisation, M. In an unmagnetised material, M = 0, but some of the domains remain aligned over small regions in the material once the magnetic field is removed. The effect of applying a magnetising force to the material is to align some of the domains to produce a non-zero magnetisation value.
Once the magnetising force has been removed, the magnetism within the material will either remain or decay away quiet quickly depending on the magnetic material being used. This ability of a material to retain its magnetism is called Retentivity and materials which are required to retain their magnetism will have a high retentivity and are used to make permanent magnets, while those materials required to loose their magnetism quickly such as soft iron cores for relays and solenoids will have a very low retentivity.

Magnetic Flux

All magnets, no matter what their shape, have two regions called magnetic poles with the magnetism both in and around a magnetic circuit producing a definite chain of organised and balanced pattern of invisible lines of flux around it. These lines of flux are collectively referred to as the "magnetic field" of the magnet. The shape of this magnetic field is more intense in some parts than others with the area of the magnet that has the greatest magnetism being called "poles". At each end of a magnet is a pole.
These lines of flux (called a vector field) can not be seen by the naked eye, but they can be seen visually by using iron fillings sprinkled onto a sheet of paper or by using a small compass to trace them out. Magnetic poles are always present in pairs, there is always a region of the magnet called the North-pole and there is always an opposite region called the South-pole.
Magnetic fields are always shown visually as lines of force that give a definite pole at each end of the material where the flux lines are more dense and concentrated. The lines which go to make up a magnetic field showing the direction and intensity are called Lines of Force or more commonly "Magnetic Flux" and are given the Greek symbol, PhiΦ ) as shown below.

Lines of Force from a Bar Magnets Magnetic Field

Lines of Force of a Magnetic Field

As shown above, the magnetic field is strongest near to the poles of the magnet were the lines of flux are more closely spaced. The general direction for the magnetic flux flow is from the NorthN ) to the SouthS ) pole. In addition, these magnetic lines form closed loops that leave at the north pole of the magnet and enter at the south pole. Magnetic poles are always in pairs.
However, magnetic flux does not actually flow from the north to the south pole or flow anywhere for that matter as magnetic flux is a static region around a magnet in which the magnetic force exists. In other words magnetic flux does not flow or move it is just there and is not influenced by gravity. Some important facts emerge when plotting lines of force:
  • 1.  -  Lines of force NEVER cross.
  • 2.  -  Lines of force are CONTINUOUS.
  • 3.  -  Lines of force always form individual CLOSED LOOPS around the magnet.
  • 4.  -  Lines of force have a definite DIRECTION from North to South.
  • 5.  -  Lines of force that are close together indicate a STRONG magnetic field.
  • 6.  -  Lines of force that are farther apart indicate a WEAK magnetic field.
Magnetic forces attract and repel like electric forces and when two lines of force are brought close together the interaction between the two magnetic fields causes one of two things to occur:
  • 1.  -  When adjacent poles are the same, (north-north or south-south) they REPEL each other.
  • 2.  -  When adjacent poles are not the same, (north-south or south-north) they ATTRACT each other.
It can be remembered by the famous expression that "opposites attract" and this interaction of magnetic fields is easily demonstrated with iron fillings. The effect upon the magnetic fields of the various combinations of poles as like poles repel and unlike poles attract can be seen below.

Magnetic Field of Like and Unlike Poles

Like and Unlike Magnetic Poles

When plotting magnetic field lines with a compass it will be seen that the lines of force are produced in such a way as to give a definite pole at each end of the magnet where the lines of force leave the North pole and re-enter at the South pole. Magnetism can be destroyed by heating or hammering the magnetic material, but cannot be destroyed or isolated by simply breaking the magnet into two pieces.
So if you take a normal bar magnet and break it into two pieces, you do not have two halves of a magnet but instead each broken piece will somehow have its own North pole and a South pole. If you take one of those pieces and break it into two again, each of the smaller pieces will have a North pole and a South pole and so on. No matter how small the pieces of the magnet become, each piece will still have a North pole and a South pole, crazy!.
Then in order for us to make use of magnetism in electrical or electronic calculations, it is necessary to define what are the various aspects of magnetism.

The Magnitude of Magnetism

We now know that the lines of force or more commonly the magnetic flux around a magnetic material is given the Greek symbol, Phi, ( Φ ) with the unit of flux being the Weber, ( Wb ) after Wilhelm Eduard Weber. But the number of lines of force within a given unit area is called the "Flux Density" and since flux ( Φ ) is measured in ( Wb ) and area ( A ) in metres squared, ( m2 ), flux density is therefore measured in Webers/Metre2 or ( Wb/m2 ) and is given the symbol B.
However, when referring to flux density in magnetism, flux density is given the unit of the Tesla after Nikola Tesla so therefore one Wb/m2 is equal to one Tesla, 1Wb/m2 = 1T. Flux density is proportional to the lines of force and inversely proportional to area so we can define Flux Density as:

Magnetic Flux Density

Magnetic Flux Density Equation
The symbol for magnetic flux density is B and the unit of magnetic flux density is the Tesla, T.
Flux Density Equation
It is important to remember that all calculations for flux density are done in the same units, e.g., flux in webers, area in m2 and flux density in Teslas.

Example No1

The amount of flux present in a round magnetic bar was measured at 0.013 webers. If the material has a diameter of 12cm, calculate the flux density.
The cross sectional area of the magnetic material in m2 is given as:
Cross-sectional Area Equation
The magnetic flux is given as 0.013 webers, therefore the flux density can be calculated as:
Flux Density
So the flux density is calculated as 1.15 Teslas.
When dealing with magnetism in electrical circuits it must be remembered that one Tesla is the density of a magnetic field such that a conductor carrying 1 ampere at right angles to the magnetic field experiences a force of one newton-metre length on it and this will be demonstrated in the next tutorial about Electromagnetism.


In the last tutorial about Magnetism we looked briefly at how permanent magnets produce a magnetic field around themselves from their north pole to their south pole. While permanent magnets produce a good and sometimes very strong static magnetic field in some applications the strength of this field is still too weak or we need to be able to control the amount of magnetic flux that is present.
So in order to obtain a much stronger and more controllable magnetic field we need to use electricity. By using coils of wire wrapped or wound around a soft magnetic material such as an iron core we can produce very strong electromagnets for use in may different applications. This then produces a relationship between magnetism and electricity that gives us another form of magnetism called Electromagnetism.
Electromagnetism is produced when an electrical current flows through a simple conductor such as a piece of wire or cable. A small magnetic field is created around the conductor with the direction of this magnetic field with regards to its "North" and "South" poles being determined by the direction of the current flowing through the conductor. Therefore, it is necessary to establish a relationship between current flowing in the conductor and the resultant magnetic field produced by this current flow and thereby defining the definite relationship that exists between Electricity and Magnetism in the form of Electromagnetism.
When an electrical current flows through a conductor a circular electromagnetic field is generated around it. The direction of rotation of this magnetic field is governed by the direction of the current flowing through the conductor with the corresponding magnetic field produced being stronger near to the centre of the current carrying conductor and weaker farther away from it as shown below.

Magnetic Field around a Conductor

Magnetic Field around a Conductor

Woodscrew Action
A simple way to determine the direction of the magnetic field around the conductor is to consider screwing an ordinary wood screw into a sheet of paper. As the screw enters the paper the rotational action is CLOCKWISE and the only part of the screw that is visible above the paper is the screw head. If the wood screw is of the pozidriv or philips type head design,the cross on the head will be visible and it is this cross that is used to indicate current flowing "into" the paper and away from the observer.
Likewise, the action of removing the screw is the reverse, anti-clockwise. As the current enters from the top it therefore leaves the underside of the paper and the only part of the wood screw that is visible from below is the tip or point of the screw and it is this point which is used to indicate current flowing "out of" the paper and towards the observer.
Then the physical action of screwing into and out of the paper indicates the direction of the current in the conductor and therefore, the direction of rotation of the electromagnetic field around it as shown below. This concept is known generally as the Right Hand Screw Action.

The Right Hand Screw Action

Right Hand Screw Action
A magnetic field implies the existence of poles and the polarity of a current carrying conductor can be established by drawing the capital letters S and N and then adding arrow heads to the free end of the letters as shown above giving a visual representation of the magnetic field direction.
Another more familiar concept which determines both the direction of current flow and the resulting direction of the magnetic flux around the conductor is called the "Left Hand Rule".
Left hand Rule of Electromagnetism
Left Hand Rule of Electromagnetism
The direction of the magnetic field is from north pole to south pole and can be deduced by holding the current carrying conductor in your left hand with the thumb extended it will be pointing in the direction of the electron flow from negative to positive. The position of the fingers laid across the conductor will now point in the direction of the magnetic lines of force as shown.

If the direction of the electron flowing through the conductor is reversed, the left hand will need to be placed onto the other side of the conductor with the thumb pointing in the new direction of the electron current flow. Also as the current is reversed the direction of the magnetic field produced around the conductor will also be reversed.
This "Left Hand Rule" can also be used to determine the magnetic direction of the poles in an electromagnetic coil. This time, the fingers point in the direction of the electron flow from negative to positive while the extended thumb indicating the direction of the north pole. There is a variation on this rule called the "right hand rule" which is based on so-called conventional current flow, (positive to negative).
When a single straight piece of wire is bent into the form of a single loop as shown below, the current will be flowing in opposite directions through the paper such that a clockwise field and an anticlockwise field are produced next to each other. The resulting space between these two conductors becomes an "intensified" magnetic field with the lines of force spreading out in such a way that they assume the form of a bar magnet generating a distinctive north and south pole at the point of intersection.

Electromagnetism around a Loop

Magnetic Field around a Loop
Lines of Force around the Loop
Lines of Force around the Loop
The current flowing through the two parallel conductors of the loop are in opposite directions as the current through the loop exits the left hand side and returns on the right hand side. This results in the magnetic field around each conductor inside the loop being in the "SAME" direction to each other.
The resulting lines of force generated by the current flowing through the loop oppose each other in the space between the two conductors where the two like poles meet thereby deforming the lines of force around each conductor as shown.
However, the distortion of the magnetic flux in between the two conductors results in an intensity of the magnetic field at the middle junction were the lines of force become closer together. The resulting interaction between the two like fields produces a mechanical force between the two conductors as they try to repel away from each other producing motion.

However, as the conductors cannot move, the two magnetic fields therefore help each other by generating a north and a south pole along this line of interaction. This results in the magnetic field being strongest in the middle between the two conductors. The intensity of the magnetic field around the conductor is proportional to the distance from the conductor and by the amount of current flowing through it.

The magnetic field generated by a straight length of current-carrying wire is very weak even with a high current passing through it. However, if several loops of wire are wound together along the same axis producing a coil, the resultant magnetic field will become even more stronger than the single loop producing an electromagnetic coil more commonly called a Solenoid. Then every coil of wire uses the effect of electromagnetism when an electrical current flows through it and we will look at this effect in more detail in the next tutorial.

The Electromagnet

We now know that a straight current carrying conductor produces a circular magnetic field around itself at all points along its length and that the direction of rotation of this magnetic field depends upon the direction of current flow through the conductor, the Left Hand Rule. In the last tutorial about Electromagnetism we saw that if we bend the conductor into a single loop the current will flow in opposite directions through the loop producing a clockwise field and an anticlockwise field next to each other. The Electromagnet uses this principal by having several individual loops magnetically joined together to produce a single coil.
Electromagnets are basically coils of wire which behave like bar magnets with a distinct north and south pole when current passes through them. The static magnetic field produced by each individual coil loop is summed with its neighbour with the combined magnetic field concentrated like the single wire loop we looked at in the last tutorial in the centre of the coil. The resultant static magnetic field with a north pole at one end and a south pole at the other is uniform and a lot more stronger in the centre of the coil than around the exterior.

Lines of Force around Electromagnets

Electromagnetic Coil

The magnetic field that this produces is stretched out in a form of a bar magnet giving a distinctive north and south pole with the flux being proportional to the amount of current flowing in the coil. If additional layers of wire are wound upon the same coil with the same current flowing, the magnetic field strength will be increased. It can be seen from this therefore that the amount of flux available in any given magnetic circuit is directly proportional to the current flowing through it and the number of turns of wire within the coil. This relationship is called Magneto Motive Force or m.m.f. and is defined as:
Magneto Motive Force Equation
Magneto Motive Force is expressed as a current, I flowing through a coil of N turns. The magnetic field strength of an electromagnet is therefore determined by the ampere turns of the coil with the more turns of wire in the coil the greater will be the strength of the magnetic field.

The Magnetic Strength of the Electromagnet

We now know that were two adjacent conductors are carrying current, magnetic fields are set up according to the direction of the current flow. The resulting interaction of the two fields is such that a mechanical force is experienced by the two conductors. When the current is flowing in the same direction (the same side of the coil) the field between the two conductors is weak causing a force of attraction as shown above. Likewise, when the current is flowing in opposite directions the field between them becomes intensified and the conductors are repelled.
The intensity of this field around the conductor is proportional to the distance from it with the strongest point being next to the conductor and progressively getting weaker further away from the conductor. In the case of a single straight conductor, the current flowing and the distance from it are factors which govern the intensity of the field. The formula therefore for calculating the "Magnetic Field Strength", H sometimes called "Magnetising Force" of a long straight current carrying conductor is derived from the current flowing through it and the distance from it.

Magnetic Field Strength for Electromagnets

Magnetising Force for Electromagnets
  • Where:
  • H - is the strength of the magnetic field in ampere-turns/metre, At/m
  • N - is the number of turns of the coil
  • I - is the current flowing through the coil in amps, A
  • L - is the length of the coil in metres, m
Then to summarise, the strength or intensity of a coils magnetic field depends on the following factors.
  • 1). The number of turns of wire within the coil.
  • 2). The amount of current flowing in the coil.
  • 3). The type of core material.
The magnetic field strength of the electromagnet also depends upon the type of core material being used as the main purpose of the core is to concentrate the magnetic flux in a well defined and predictable path. So far only air cored (hollow) coils have been considered but the introduction of other materials into the core (the centre of the coil) has a very large controlling effect on the strength of the magnetic field.
Electromagnet using a nail
If the material is non-magnetic for example wood, for calculation purposes it can be regarded as free space as they have very low values of permeability. If however, the core material is made from a Ferromagnetic material such as iron, nickel, cobalt or any mixture of their alloys, a considerable difference in the flux density around the coil will be observed.
Ferromagnetic materials are those which can be magnetised and are usually made from soft iron, steel or various nickel alloys. The introduction of this type of material into a magnetic circuit has the effect of concentrating the magnetic flux making it more concentrated and dense and amplifies the magnetic field created by the current in the coil.
We can prove this by wrapping a coil of wire around a large soft-iron nail and connecting it to a battery as shown. This simple classroom experiment allows us to pick-up a large quantity of clips or pins and we can make the electromagnet stronger by adding more turns to the coil. This degree of intensity of the magnetic field either by a hollow air core or by introducing ferromagnetic materials into the core is called Magnetic Permeability.

Permeability of Electromagnets

If cores of different materials with the same physical dimensions are used in the electromagnet, the strength of the magnet will vary in relation to the core material being used. This variation in the magnetic strength is due to the number of flux lines passing through the central core. if the magnetic material has a high permeability then the flux lines can easily be created and pass through the central core and permeability (μ) and it is a measure of the ease by which the core can be magnetised.
The numerical constant given for the permeability of a vacuum is given as: μo = 4.π.10-7 H/m with the relative permeability of free space (a vacuum) generally given a value of one. It is this value that is used as a reference in all calculations dealing with permeability and all materials have their own specific values of permeability. The problem with using just the permeability of different iron, steel or alloy cores is that the calculations involved can become very large so it is more convenient to define the materials by their relative permeability.
Relative Permeability, symbol μr is the product of μ (absolute permeability) and μo the permeability of free space and is given as.

Relative Permeability

Relative Permeability
Materials that have a permeability slightly less than that of free space (a vacuum) and have a weak, negative susceptibility to magnetic fields are said to be Diamagnetic in nature such as: water, copper, silver and gold. Those materials with a permeability slightly greater than that of free space and themselves are only slightly attracted by a magnetic field are said to be Paramagnetic in nature such as: gases, magnesium, and tantalum.

Example No1

The absolute permeability of a soft iron core is given as 80 milli-henries/m (80.10-3). Calculate the equivalent relative permeability value.
Relative Permeability
When ferromagnetic materials are used in the core the use of relative permeability to define the field strength gives a better idea of the strength of the magnetic field for the different types of materials used. For example, a vacuum and air have a relative permeability of one and for an iron core it is around 500, so we can say that the field strength of an iron core is 500 times stronger than an equivalent hollow air coil and this relationship is much easier to understand than 0.628x10-3 H/m, ( 500.4.π.10-7).
While, air may have a permeability of just one, some ferrite and permalloy materials can have a permeability of 10,000 or more. However, there are limits to the amount of magnetic field strength that can be obtained from a single coil as the core becomes heavily saturated as the magnetic flux increases and this is looked at in the next tutorial about B-H curves and Hysteresis.

Magnetic Hysteresis

The lag or delay of a magnetic material known commonly as Magnetic Hysteresis, relates to the magnetisation properties of a material by which it firstly becomes magnetised and then de-magnetised. We know that the magnetic flux generated by an electromagnetic coil is the amount of magnetic field or lines of force produced within a given area and that it is more commonly called "Flux Density". Given the symbol B with the unit of flux density being the Tesla, T.
We also know from the previous tutorials that the magnetic strength of an electromagnet depends upon the number of turns of the coil, the current flowing through the coil or the type of core material being used, and if we increase either the current or the number of turns we can increase the magnetic field strength, symbol H.
Previously, the relative permeability, symbol μr was defined as the product of the absolute permeability μ and the permeability of free space μo (a vacuum) and this was given as a constant. However, the relationship between the flux density, B and flux density, H can be defined by the fact that the relative permeability, μr is not a constant but a function of the magnetic field intensity thereby giving magnetic flux density as:  B = μ H. Then the magnetic flux density in the material will be increased by a larger factor as a result of its relative permeability for the material compared to the magnetic flux density in vacuum, μoH and for an air-cored coil this relationship is given as:
Flux Density and Magnetising Force Equations
So for ferromagnetic materials the ratio of flux density to field strength (B/H) is not constant but varies with flux density. However, for air cored coils or any non-magnetic medium core such as woods or plastics, this ratio can be considered as a constant and this constant is known as μo, the permeability of free space, (μo = 4.π.10-7 H/m). By plotting values of flux density, (B) against the field strength, (H) we can produce a set of curves called Magnetisation Curves, Magnetic Hysteresis Curves or more commonly B-H Curves for each type of core material used as shown below.

Magnetisation or B-H Curve

The Magnetisation Hysteresis B-H Curve

The set of magnetisation curves, M above represents an example of the relationship between B and H for soft-iron and steel cores but every type of core material will have its own set of magnetic hysteresis curves. You may notice that the flux density increases in proportion to the field strength until it reaches a certain value were it can not increase any more becoming almost level and constant as the field strength continues to increase.
This is because there is a limit to the amount of flux density that can be generated by the core as all the domains in the iron are perfectly aligned. Any further increase will have no effect on the value of M, and the point on the graph where the flux density reaches its limit is called Magnetic Saturation also known as Saturation of the Core and in our simple example above the saturation point of the steel curve begins at about 3000 ampere-turns per metre.
Saturation occurs because as we remember from the previous Magnetism tutorial which included Weber's theory, the random haphazard arrangement of the molecule structure within the core material changes as the tiny molecular magnets within the material become "lined-up". As the magnetic field strength, (H) increases these molecular magnets become more and more aligned until they reach perfect alignment producing maximum flux density and any increase in the magnetic field strength due to an increase in the electrical current flowing through the coil will have little or no effect.


Lets assume that we have an electromagnetic coil with a high field strength due to the current flowing through it, and that the ferromagnetic core material has reached its saturation point, maximum flux density. If we now open a switch and remove the magnetising current flowing through the coil we would expect the magnetic field around the coil to disappear as the magnetic flux reduced to zero.
However, the magnetic flux does not completely disappear as the electromagnetic core material still retains some of its magnetism even when the current has stopped flowing in the coil. This ability to retain some magnetism in the core after magnetisation has stopped is called Retentivity or Remanence while the amount of flux density still present in the core is called Residual Magnetism, BR .
The reason for this that some of the tiny molecular magnets do not return to a completely random pattern and still point in the direction of the original magnetising field giving them a sort of "memory". Some ferromagnetic materials have a high retentivity (magnetically hard) making them excellent for producing permanent magnets.
While other ferromagnetic materials have low retentivity (magnetically soft) making them ideal for use in electromagnets, solenoids or relays. One way to reduce the this residual flux density to zero is to reverse the direction of current flow through the coil making the value of H, the magnetic field strength negative and this is called a Coercive Force, HC .
If this reverse current is increased further the flux density will also increase in the reverse direction until the ferromagnetic core reaches saturation again but in the reverse direction from before. Reducing the magnetising current, i once again to zero will produce a similar amount of residual magnetism but in the reverse direction. Then by constantly changing the direction of the magnetising current through the coil from a positive direction to a negative direction, as would be the case in an AC supply, a Magnetic Hysteresis loop of the ferromagnetic core can be produced.

Magnetic Hysteresis Loop

Magnetic Hysteresis Loop
The Magnetic Hysteresis loop above, shows the behavior of a ferromagnetic core graphically as the relationship between B and H is non-linear. Starting with an unmagnetised core both B and H will be at zero, point 0 on the magnetisation curve.
If the magnetisation current, i is increased in a positive direction to some value the magnetic field strength H increases linearly with i and the flux density B will also increase as shown by the curve from point 0 to point a as it heads towards saturation. Now if the magnetising current in the coil is reduced to zero the magnetic field around the core reduces to zero but the magnetic flux does not reach zero due to the residual magnetism present within the core and this is shown on the curve from point a to point b.
To reduce the flux density at point b to zero we need to reverse the current flowing through the coil. The magnetising force which must be applied to null the residual flux density is called a "Coercive Force". This coercive force reverses the magnetic field re-arranging the molecular magnets until the core becomes unmagnetised at point c. An increase in the reverse current causes the core to be magnetised in the opposite direction and increasing this magnetisation current will cause the core to reach saturation but in the opposite direction, point d on the cure which is symmetrical to point b. If the magnetising current is reduced again to zero the residual magnetism present in the core will be equal to the previous value but in reverse at point e.
Again reversing the magnetising current flowing through the coil this time into a positive direction will cause the magnetic flux to reach zero, point f on the curve and as before increasing the magnetisation current further in a positive direction will cause the core to reach saturation at point a. Then the B-H curve follows the path of a-b-c-d-e-f-a as the magnetising current flowing through the coil alternates between a positive and negative value such as the cycle of an AC voltage. This path is called a Magnetic Hysteresis Loop.
The effect of magnetic hysteresis shows that the magnetisation process of a ferromagnetic core and therefore the flux density depends on which part of the curve the ferromagnetic core is magnetised on as this depends upon the circuits past history giving the core a form of "memory". Then ferromagnetic materials have memory because they remain magnetised after the external magnetic field has been removed. However, soft ferromagnetic materials such as iron or silicon steel have very narrow magnetic hysteresis loops resulting in very small amounts of residual magnetism making them ideal for use in relays, solenoids and transformers as they can be easily magnetised and demagnetised.
Since a coercive force must be applied to overcome this residual magnetism, work must be done in closing the hysteresis loop with the energy being used being dissipated as heat in the magnetic material. This heat is known as hysteresis loss, the amount of loss depends on the material's value of coercive force. By adding addictive's to the iron metal such as silicon, materials with a very small coercive force can be made that have a very narrow hysteresis loop. Materials with narrow hysteresis loops are easily magnetised and demagnetised and known as soft magnetic materials.

Magnetic Hysteresis Loops for Soft and Hard Materials

A Magnetic Hysteresis Loop for Soft and Hard Ferromagnetic Materials
Magnetic Hysteresis results in the dissipation of wasted energy in the form of heat with the energy wasted being in proportion to the area of the magnetic hysteresis loop. Hysteresis losses will always be a problem in AC transformers where the current is constantly changing direction and thus the magnetic poles in the core will cause losses because they constantly reverse direction.
Rotating coils in DC machines will also incur hysteresis losses as they are alternately passing north the south magnetic poles. As said previously, the shape of the hysteresis loop depends upon the nature of the iron or steel used and in the case of iron which is subjected to massive reversals of magnetism, for example transformer cores, it is important that the B-H hysteresis loop is as small as possible.
In the next tutorial about Electromagnetism, we will look at Faraday's Law of Electromagnetic Induction and see that by moving a wire conductor within a stationary magnetic field it is possible to induce an electric current in the conductor producing a simple generator.

Electromagnetic Induction

Air-core Electromagnetic Coil
Air-core Hollow Coil
We have seen previously that when a DC current pass through a long straight conductor a magnetising force, H and a static magnetic field, B is developed around the wire. If the wire is then wound into a coil, the magnetic field is greatly intensified producing a static magnetic field around itself forming the shape of a bar magnet giving a distinct North and South pole.
The magnetic flux developed around the coil being proportional to the amount of current flowing in the coils windings as shown. If additional layers of wire are wound upon the same coil with the same current flowing, the static magnetic field strength will be increased and therefore, the magnetic field strength of a coil is determined by the ampere turns of the coil with the more turns of wire within the coil the greater will be the strength of the static magnetic field around it.
But what if we reversed this idea by disconnecting the electrical current from the coil and instead of a hollow core we placed a bar magnet inside the core of the coil of wire. By moving this bar magnet "in" and "out" of the coil a current would be induced into the coil by the physical movement of the magnetic flux inside it.
Likewise, if we kept the bar magnet stationary and moved the coil back and forth within the magnetic field an electric current would be induced in the coil. Then by either moving the wire or changing the magnetic field we can induce a voltage and current within the coil and this process is known as Electromagnetic Induction and is the basic principal of operation of transformers, motors and generators.
Electromagnetic Induction was first discovered way back in the 1830's by Michael Faraday. Faraday noticed that when he moved a permanent magnet in and out of a coil or a single loop of wire it induced an ElectroMotive Force or emf, in other words a Voltage, and therefore a current was produced. So what Michael Faraday discovered was a way of producing an electrical current in a circuit by using only the force of a magnetic field and not batteries. This then lead to a very important law linking electricity with magnetism, Faraday's Law of Electromagnetic Induction. So how does this work?.
When the magnet shown below is moved "towards" the coil, the pointer or needle of the Galvanometer, which is basically a very sensitive centre zero'ed moving-coil ammeter, will deflect away from its centre position in one direction only. When the magnet stops moving and is held stationary with regards to the coil the needle of the galvanometer returns back to zero as there is no physical movement of the magnetic field.
Likwwise, when the magnet is moved "away" from the coil in the other direction, the needle of the galvanometer deflects in the opposite direction with regards to the first indicating a change in polarity. Then by moving the magnet back and forth towards the coil the needle of the galvanometer will deflect left or right, positive or negative, relative to the directional motion of the magnet.

Electromagnetic Induction by a Moving Magnet

Electromagnetic Induction by a Moving Magnet
Likewise, if the magnet is now held stationary and ONLY the coil is moved towards or away from the magnet the needle of the galvanometer will also deflect in either direction. Then the action of moving a coil or loop of wire through a magnetic field induces a voltage in the coil with the magnitude of this induced voltage being proportional to the speed or velocity of the movement.
Then we can see that the faster the movement of the magnetic field the greater will be the induced emf or voltage in the coil, so for Faraday's law to hold true there must be "relative motion" or movement between the coil and the magnetic field and either the magnetic field, the coil or both can move.

Faraday's Law of Induction

From the above description we can say that a relationship exists between an electrical voltage and a changing magnetic field to which Michael Faraday's famous law of electromagnetic induction states:
"that a voltage is induced in a circuit whenever relative motion exists between a conductor and a magnetic field and that the magnitude of this voltage is proportional to the rate of change of the flux".
In other words, Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a closed circuit, a current.
So how much voltage (emf) can be induced into the coil using just magnetism. Well this is determined by the following 3 different factors.
  • 1). Increasing the number of turns of wire in the coil. - By increasing the amount of individual conductors cutting through the magnetic field, the amount of induced emf produced will be the sum of all the individual loops of the coil, so if there are 20 turns in the coil there will be 20 times more induced emf than in one piece of wire.
  • 2). Increasing the speed of the relative motion between the coil and the magnet. - If the same coil of wire passed through the same magnetic field but its speed or velocity is increased, the wire will cut the lines of flux at a faster rate so more induced emf would be produced.
  • 3). Increasing the strength of the magnetic field. - If the same coil of wire is moved at the same speed through a stronger magnetic field, there will be more emf produced because there are more lines of force to cut.
If we were able to move the magnet in the diagram above in and out of the coil at a constant speed and distance without stopping we would generate a continuously induced voltage that would alternate between one positive polarity and a negative polarity producing an alternating or AC output voltage and this is the basic principal of how a Generator works similar to those used in dynamos and car alternators.
In small generators such as a bicycle dynamo, a small permanent magnet is rotated by the action of the bicycle wheel inside a fixed coil. Alternatively, an electromagnet powered by a fixed DC voltage can be made to rotate inside a fixed coil, such as in large power generators producing in both cases an alternating current.

Simple Generator using Magnetic Induction

Basic Generator using Magnetic Induction
The simple dynamo type generator above consists of a permanent magnet which rotates around a central shaft with a coil of wire placed next to this rotating magnetic field. As the magnet spins, the magnetic field around the top and bottom of the coil constantly changes between a north and a south pole. This rotational movement of the magnetic field results in an alternating emf being induced into the coil as defined by Faraday's law of electromagnetic induction.
The magnitude of the electromagnetic induction is directly proportional to the flux density, β the number of loops giving a total length of the conductor, l in meters and the rate or velocity, ν at which the magnetic field changes within the conductor in meters/second or m/s, giving by the motional emf expression:

Faraday's Motional emf Expression

Induced emf Voltage
If the conductor does not move at right angles (90°) to the magnetic field then the angle θ° will be added to the above expression giving a reduced output as the angle increases:
EMF Voltage not at Right-angles to the Flux

Lenz's Law of Electromagnetic Induction

Faraday's Law tells us that inducing a voltage into a conductor can be done by either passing it through a magnetic field, or by moving the magnetic field past the conductor and that if this conductor is part of a closed circuit, an electric current will flow. This voltage is called an induced emf as it has been induced into the conductor by a changing magnetic field due to electromagnetic induction with the negative sign in Faraday's law telling us the direction of the induced current (or polarity of the induced emf).
But a changing magnetic flux produces a varying current through the coil which itself will produce its own magnetic field as we saw in the Electromagnets tutorial. This self-induced emf opposes the change that is causing it and the faster the rate of change of current the greater is the opposing emf. This self-induced emf will, by Lenz’s law oppose the change in current in the coil and because of its direction this self-induced emf is generally called a back-emf.
Lenz's Law states that: the direction of an induced emf is such that it will always opposes the change that is causing it". In other words, an induced current will always OPPOSE the motion or change which started the induced current in the first place and this idea is found in the analysis of Inductance. Likewise, if the magnetic flux is decreased then the induced emf will oppose this decrease by generating and induced magnetic flux that adds to the original flux.
Lenz's law is one of the basic laws in electromagnetic induction for determining the direction of flow of induced currents and is related to the law of conservation of energy. According to the law of conservation of energy which states that the total amount of energy in the universe will always remain constant as energy can not be created nor destroyed. Lenz's law is derived from Michael Faraday's law of induction.
One final comment about Lenz's Law regarding electromagnetic induction. We now know that when a relative motion exists between a conductor and a magnetic field, an emf is induced within the conductor. But the conductor may not actually be part of the coils electrical circuit, but may be the coils iron core or some other metallic part of the system, for example, a transformer. The induced emf within this metallic part of the system causes a circulating current to flow around it and this type of core current is known as an Eddy Current.
Eddy currents generated by electromagnetic induction circulate around the coils core or any connecting metallic components inside the magnetic field because for the magnetic flux they are acting like a single loop of wire. Eddy currents do not contribute anything towards the usefulness of the system but instead they oppose the flow of the induced current by acting like a negative force generating resistive heating and power loss within the core. However, there are electromagnetic induction furnace applications in which only eddy currents are used to heat and melt ferromagnetic metals.

Eddy Currents Circulating in a Transformer

Eddy Currents in a Transformer
The changing magnetic flux in the iron core of a transformer above will induce an emf, not only in the primary and secondary windings, but also in the iron core. The iron core is a good conductor, so the currents induced in a solid iron core will be large. Furthermore, the eddy currents flow in a direction which, by Lenz's law, acts to weaken the flux created by the primary coil. Consequently, the current in the primary coil required to produce a given B field is increased, so the hysteresis curves are fatter along the H axis.
Laminating the Core
Laminating the Iron Core
Eddy current and hysteresis losses can not be eliminated completely, but they can be greatly reduced. Instead of having a solid iron core as the magnetic core material of the transformer or coil, the magnetic path is "laminated".
These laminations are very thin strips of insulated (usually with varnish) metal joined together to produce a solid core. The laminations increase the resistance of the iron-core thereby increasing the overall resistance to the flow of the eddy currents, so the induced eddy current power-loss in the core is reduced, and it is for this reason why the magnetic iron circuit of transformers and electrical machines are all laminated.


The Hall Effect Device

We could not end this section on Magnetism without a mention about magnetic sensors and especially the Hall Effect Sensor. Magnetic sensors convert magnetic or magnetically encoded information into electrical signals for processing by electronic circuits, and in the Sensors and Transducers tutorials we looked at inductive proximity sensors and the LDVT as well as solenoid and relay output actuators.
Magnetic sensors are solid state devices that are becoming more and more popular because they can be used in many different types of application such as sensing position, velocity or directional movement. They are also a popular choice of sensor for the electronics designer due to their non-contact wear free operation, their low maintenance, robust design and as sealed hall effect devices are immune to vibration, dust and water.
One of the main uses of magnetic sensors is in automotive systems for the sensing of position, distance and speed. For example, the angular position of the crank shaft for the firing angle of the spark plugs, the position of the car seats and seat belts for air-bag control or wheel speed detection for the anti-lock braking system, (ABS). Magnetic sensors are designed to respond to a wide range of positive and negative magnetic fields in a variety of different applications and one type of magnet sensor whose output signal is a function of magnetic field density around it is called the Hall Effect Sensor.
Hall Effect Sensors are devices which are activated by an external magnetic field. We know that a magnetic field has two important characteristics flux density, (B) and polarity (North and South Poles). The output signal from a Hall effect sensor is the function of magnetic field density around the device. When the magnetic flux density around the sensor exceeds a certain preset threshold, the sensor detects it and generates an output voltage called the Hall Voltage, VH. Consider the diagram below.

Hall Effect Sensor

Hall Effect Sensor

Hall Effect Sensors consist basically of a thin piece of rectangular p-type semiconductor material such as gallium arsenide (GaAs), indium antimonide (InSb) or indium arsenide (InAs) passing a continuous current through itself. When the device is placed within a magnetic field, the magnetic flux lines exert a force on the semiconductor material which deflects the charge carriers, electrons and holes, to either side of the semiconductor slab. This movement of charge carriers is a result of the magnetic force they experience passing through the semiconductor material.
As these electrons and holes move side wards a potential difference is produced between the two sides of the semiconductor material by the build-up of these charge carriers. Then the movement of electrons through the semiconductor material is affected by the presence of an external magnetic field which is at right angles to it and this effect is greater in a flat rectangular shaped material.
The effect of generating a measurable voltage by using a magnetic field is called the Hall Effect after Edwin Hall who discovered it back in the 1870's with the basic physical principle underlying the Hall effect being Lorentz force. To generate a potential difference across the device the magnetic flux lines must be perpendicular, (90o) to the flow of current and be of the correct polarity, generally a south pole.
The Hall effect provides information regarding the type of magnetic pole and magnitude of the magnetic field. For example, a south pole would cause the device to produce a voltage output while a north pole would have no effect. Generally, Hall Effect sensors and switches are designed to be in the "OFF", (open circuit condition) when there is no magnetic field present. They only turn "ON", (closed circuit condition) when subjected to a magnetic field of sufficient strength and polarity.

Hall Effect Magnetic Sensor

The output voltage, called the Hall voltage, (VH) of the basic Hall Element is directly proportional to the strength of the magnetic field passing through the semiconductor material (output  H). This output voltage can be quite small, only a few microvolts even when subjected to strong magnetic fields so most commercially available Hall effect devices are manufactured with built-in DC amplifiers, logic switching circuits and voltage regulators to improve the sensors sensitivity, hysteresis and output voltage. This also allows the Hall effect sensor to operate over a wider range of power supplies and magnetic field conditions.

Hall Effect Sensor

Hall Effect Sensor
Hall Effect Sensors are available with either linear or digital outputs. The output signal for linear (analogue) sensors is taken directly from the output of the operational amplifier with the output voltage being directly proportional to the magnetic field passing through the Hall sensor. This output Hall voltage is given as:
Hall Voltage

  • Where:
  • VH is the Hall Voltage in volts
  • RH is the Hall Effect co-efficient
  • I is the current flow through the sensor in amps
  • t is the thickness of the sensor in mm
  • B is the Magnetic Flux density in Teslas
Linear Output Voltage
Linear or analogue sensors give a continuous voltage output that increases with a strong magnetic field and decreases with a weak magnetic field. In linear output Hall effect sensors, as the strength of the magnetic field increases the output signal from the amplifier will also increase until it begins to saturate by the limits imposed on it by the power supply. Any additional increase in the magnetic field will have no effect on the output but drive it more into saturation.
Digital output sensors on the other hand have a Schmitt-trigger with built in hysteresis connected to the op-amp. When the magnetic flux passing through the Hall sensor exceeds a preset value the output from the device switches quickly between its "OFF" condition to an "ON" condition without any type of contact bounce. This built-in hysteresis eliminates any oscillation of the output signal as the sensor moves in and out of the magnetic field. Then digital output sensors have just two states, "ON" and "OFF".
There are two basic types of digital Hall effect sensor, Bipolar and Unipolar. Bipolar sensors require a positive magnetic field (south pole) to operate them and a negative field (north pole) to release them while unipolar sensors require only a single magnetic south pole to both operate and release them as they move in and out of the magnetic field.
Most Hall effect devices can not directly switch large loads as their output drive capabilities are very small around 10 to 20mA. For large current loads an open-collector (current sinking) NPN Transistor is added to the output. This transistor operates in its saturated region as a NPN sink switch which shorts the output terminal to ground whenever the applied flux density is higher than that of the "ON" preset point. This output transistor can be either an open emitter, open collector or both providing a push-pull output configuration that can sink enough current to directly drive many loads, including relays, motors, LEDs, and lamps.

Hall Effect Applications

Hall effect sensors are activated by a magnetic field and in many applications the device can be operated by a single permanent magnet attached to a moving shaft or device. There are many different types of magnet movements, such as "Head-on", "Sideways", "Push-pull" or "Push-push" etc sensing movements. Which every type of configuration is used, to ensure maximum sensitivity the magnetic lines of flux must always be perpendicular to the sensing area of the device and must be of the correct polarity.
Also to ensure linearity, high field strength magnets are required that produce a large change in field strength for the required movement. There are several possible paths of motion for detecting a magnetic field, and below are two of the more common sensing configurations using a single magnet. Head-on Detection and Sideways Detection.

Head-on Detection

Head-on Hall Effect Sensing
As its name implies, head-on detection requires that the magnetic field is perpendicular to the sensing device and that for detection, it approaches the sensor straight on towards the active face. A sort of "head-on" approach.
This head-on approach generates an output signal, VH which in the linear devices represents the strength of the magnetic field, the magnetic flux density, as a function of distance away from the sensor. The nearer and therefore the stronger the magnetic field, the greater the output voltage and vice versa.
Linear devices can also differentiate between positive and negative magnetic fields. Non-linear devices can be made to trigger the output "ON" at a preset air gap distance away from the magnet for indicating positional detection.

Sideways Detection

Sideways Hall Effect Sensing
The second sensing configuration is sideways detection. This requires moving the magnet across the face of the Hall element in a sideways motion.
Sideways or slide-by detection is useful for detecting the presence of a magnetic field as it moves across the face of the Hall element within a fixed air gap distance for example, counting rotational magnets or the speed of rotation.
Depending upon the position of the magnetic field as it passes by the zero field centre line of the sensor, a linear output voltage representing both a positive and a negative output can be produced. This allows for directional movement detection which can be vertical as well as horizontal.
There are many different applications for Hall Effect Sensors especially as proximity sensors. They can be used instead of optical and light sensors were the environmental conditions consist of water, vibration, dirt or oil such as in automotive applications. Hall effect devices can also be used for current sensing.
We know from the previous tutorials that when a current passes through a conductor, a circular electromagnetic field is produced around it. By placing the Hall sensor next to the conductor, electrical currents from a few milliamps into thousands of amperes can be measured from the generated magnetic field without the need of large or expensive transformers and coils.
As well as detecting the presence or absence of magnets and magnetic fields, Hall effect sensors can also be used to detect ferromagnetic materials such as iron and steel by placing a small permanent "biasing" magnet behind the active area of the device. The sensor now sits in a permanent and static magnetic field, and any change or disturbance to this magnetic field by the introduction of a ferrous material will be detected with sensitivities as low as mV/G possible.
There are many different ways to interface Hall effect sensors to electrical and electronic circuits depending upon the type of device, whether digital or linear. One very simple and easy to construct example is using a Light Emitting Diode as shown below.

Positional Detector

Positional Indicator

This head-on positional detector will be "OFF" when there is no magnetic field present, (0 gauss). When the permanent magnets south pole (positive gauss) is moved perpendicular towards the active area of the Hall effect sensor the device turns "ON" and lights the LED. Once switched "ON" the Hall effect sensor stays "ON".
To turn the device and therefore the LED "OFF" the magnetic field must be reduced to below the release point for unipolar sensors or exposed to a magnetic north pole (negative gauss) for bipolar sensors. The LED can be replaced with a larger power transistor if the output of the Hall effect sensor is required to switch larger current loads.


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