The Electromagnetic field

The Electromagnetic field

A simple electromagnet can be created by wrapping a coil of wire around a soft iron core, such as a large nail

We now know from the previous tutorials 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.


Basically coils of wire which behave like bar magnets with a distinct north and south pole when an electrical current passes through the coil.

The static magnetic field produced by each individual coil loop is summed with its,  with the combined magnetic field concentrated like the single wire loop we looked at in the last tutorial in the cent 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 cent of the coil than around the exterior.

Lines of Force around an Electromagnet

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 “Magnetic 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

  • Where:
  • H – is the strength of the magnetic field in ampere-turns/m, 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 m

Then to , the strength or intensity of a coils magnetic field depends on the following factors.

  • The number of turns of wire within the coil.
  • The amount of current flowing in the coil.
  • 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 has a very large controlling effect on the strength of the magnetic field.

ElectromagnetElectromagnet 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 magnetic 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 magnetic.

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 equation

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 Di magnetic 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 Para magnetic in nature such as: gases, magnesium, and tantalum.

Electromagnet Example No 1

The absolute permeability of a soft iron core is given as  (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 0.628×10-3 H/m, ( 500.4.π.10-7).

While, air may have a permeability of just one, some 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.


In the Magnetism tutorial 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 magnetic 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 produce 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 many different types of electrical applications. This use of coils of wire produces a relationship between electricity and magnetism that gives us another form of magnetism called Electromagnetism.

Electromagnetism is produced when an electrical current flows through a simple conductor such as a length of wire or cable, and as current passes along the whole of the conductor then a magnetic field is created along the whole of the conductor. The small magnetic field created around the conductor has a definite direction with both the “North” and “South” poles produced being determined by the direction of the electrical current flowing through the conductor.

Therefore, it is necessary to establish a relationship between current flowing through the conductor and the resultant magnetic field produced around it by this flow of current allowing us to define the relationship that exists between Electricity and Magnetism in the form of Electromagnetism.

We have established that when an electrical current flows through a conductor a circular electromagnetic field is produced around it with the magnetic lines of flux forming complete loops that do not cross around the whole length of the conductor.

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 center of the current carrying conductor. This is because the path length of the loops being greater the further away from the conductor resulting in weaker flux lines as shown below.

Magnetic Field around a Conductor

magnetic field around conductor

wood screw 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  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, anticlockwise. 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 the wood screw in 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 two poles, a north and a south. 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”.

electromagnetism left hand ruleLeft Hand Rule of

The  direction of a magnetic field is from its north pole to its south pole. This direction can be deduced by holding the current carrying conductor in your left hand with the thumb extended pointing in the direction of the electron flow from negative to positive.

The position of the fingers laid across and around the conductor will now be pointing in the direction of the generated 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 because as we have said previously, the direction of the magnetic field depends upon the direction of current flow.

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).

Consider when a single straight piece of wire is bent into the form of a single loop as shown below. Although the electric current is flowing in the same direction through the whole length of the wire conductor, it will be flowing in opposite directions through the paper. This is because the current leaves the paper on one side and enters the paper on the other therefore a clockwise field and an anticlockwise field are produced next to each other across the sheet of paper.

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. In an electrical machine this repelling of these two magnetic fields produces 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 around a straight length of current-carrying wire is very weak even with a high current passing through it. However, if several loops of the wire are wound together along the same axis producing a coil of wire, the resultant magnetic field will become even more concentrated and stronger than that of just a single loop. This produces an electromagnetic coil more commonly called a Solenoid.

Then every length of wire has the effect of electromagnetism around itself when an electrical current flows through it. The direction of the magnetic field being  upon the direction of the flow of current. We can increase the strength of the generated magnetic field by forming the length of wire into a coil and we will look at this effect in more detail in the next tutorial.