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.

**Electromagnets** are 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 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.

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** 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.

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.

- 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.

- 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 (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**.

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: μ_{o} = 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 μ_{r} is the product of μ (absolute permeability) and μ_{o} the permeability of free space and is given as.

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.

The absolute permeability of a soft iron core is given as 80 milli-henries/m (80.10^{-3}). Calculate the equivalent relative permeability value.

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 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**.

Error! Please fill all fields.

I have a question. when using electromagnet as poles i.e. one north and one south how does the strength of the electromagnet depends? Is it the same eq. ? The type of electromagnets that are used in production of electricity. please help.

The strength of the magnetic field produced by an electromagnet depends on the number of turns of wire, the current flowing through the wire and permeability of the core.

Thank you very much for your help.

Can the flux flow through wood?If can then emf will be induced in it or not ?

No, you can not induce a voltage in wood.

Great insight on matters electronic and electrical principles

I found a way to make a electromagnet have only one side that attracts metal and the other side does nothing with metal, but attracts one pole of a normal magnet and on the other side does NOT repel any side of a normal magnet.So my question is can i conclude that i invented a monopole electromagnet? I doubt it because i’m doing only one thing fundamentally different to make it…

No, in magnetic fields the force lines are always closed so there is never a single monopole. A magnet, even an electromagnet is always made of a dipole that has two distinct poles, a north pole and a south pole. That is, magnetic poles are always found in pairs.

Your saying that when a electromagnet attrects on one side it must repel on the other side… NO i made a practical example of a rod with a “secret way of winding” that ONLY attracts ONE pole of a normal magnet on BOTH sides and does NOT repel any sides of a normal magnet. So how can it have a south pole and a north pole? And the strange thing is that only one side of my “PRACTICAL rod” attracts metal.If you’re right then i should attract metal on both sides. So i have a invention that rewrites all laws of electromagnetism..? ðŸ˜®

I wÃ nt to learn about construction of electromagnet.

What does higher and lower value of permeability suggests in case of iron core?

The magnetic field of an electromagnet is, B= Uo.n.I tesla

For using a magnetic core, the field is, B=U0.Ur.n.I tesla

If I use a high magnetic permeability material core

(metglas, relative permeability, Ur= 1 000 000_ from wikipedia source), will it multiply the field with that amount? or there is some other issue?

I’ve bought a alloy material from a commercial company. On their, website, it says that the alloy has relative permeability more than 50,000. I used that core material in a solenoid coil. but it just increase the magnetic field around 7 times higher than the magnetic field with air core. I was expecting that the core will increase the field 50,000 times than the solenoid with air core.

Am I missing some basic properties of electromagnet?

it will be really helpful if you suggest me.

Hi sir,

I’m one of the million student that your site helped. I am just confuse on the relative permeability’s formula, base on the text above the Relative Permeability with a symbol Î¼r is the PRODUCT of Î¼ (absolute permeability) and Î¼o the permeability of free space and is given as.

How come that the formula below the text shows that Relative Permeability is the ratio of the absolute permeability and the permeability of free space?

The ratio B/H is gives the permeability of free space Uo, and its value is given as: 4pi x 10^-7 H/m. So B = Uo.H in a vacuum, air or non-magnetic materials such as plastic. The relative permeability of Air is defined as: 1 (one) and the permeability of all materials are referenced from this so the relative permeability of a material is called Ur. Thus in general B = Uo.Ur.H

The actual permeability of a material (U) is found by multiplying the permeability of free space (Uo) by the relative permeability (Ur). Then U = Uo x Ur, and from that we can find the values of Uo = U/Ur or Ur = U/Uo

Hello there.

I followed the link on Hysteresis after reading there are no limits to the amount of magnetic force that can be obtained from a single cell coil. Only to find there is a limit in Hysteresis. So there a limit not infinite as suggested. Excuse my ignorance its my first day on the job ?

Hi, great page. Quick question: when you did the H=N*I / L . L is the length of the coil in metres, when you say length is that the length of the wire before turned into the coil or literally the length along the coil when turned? thanks

For a coil the magnetic field strength, H is proportional to current and is also a function of loop area defined by the conductor carrying the current. Then the magnetic strength of the coil is determined by the ampere-turns of each coil and if the magnetic circuit supporting the coil is of a uniform cross-sectional area, the magnetic field strength per metre length of the flux path is the length of one loop.