An electromagnetic field is a physical field that corresponds to the degree of action of electromagnetic energy in space and consists of a magnetic field and an electric field that are interconnected. The electric current creates a magnetic field in the area of the charged body, which affects the movement of the bodies around the charged body. An electric voltage is induced in the conductor, which moves in the magnetic field, and so the conductor (current flows through it) can move in the magnetic field = with a certain force.


The electric field cannot be separated from the magnetic field because they are related and therefore we speak of an electromagnetic field.


Maxwell’s equations (published in 1873 by the theoretical physicist James Clerk Maxwell) are the basis for the description of the electromagnetic field. These laws are natural, they do not need to be derived from other laws, however other electromagnetic field equations can be derived from them.

Toroid magnetic field

A toroid is a coil whose same turns are wound on a ring and we can imagine it as a solenoid twisted into the shape of a ring. This is a special case of a coil without magnetic poles. Its induction lines run only inside the ring as concentric circles and the created magnetic field is almost homogeneous.

Img.1 Application of Ampere’s law for a toroid


Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. The electric charge (if we take it as a basic term for the description of electromagnetism) is so fundamental that we only can talk about its properties.


The basic properties of an electric charge include the following statements:

  • there are two types of electric charge, positive (marked with a + sign) and negative (marked with a – sign),
  • electric charges have a repulsive effect on each other (charges with the same sign are repelled) or attractive (charges with the opposite sign are attracted),
  • the law of conservation of electric charge (meaning that the charge of the universe is constant),
  • a fundamental charge is the magnitude of the charge on an electron which is e=1.6×10-19C


Electromagnetism, as a part of physics, that studies the connections between electrical and magnetic aspects, did not exist. Until the end of the 18th century, electrical and magnetic energy were studied separately, because no mutual effects were observed between the events. Various important mathematicians were involved in building the theory of electromagnetism, but it was not until James Clerk Maxwell developed the pioneering theory of electromagnetism and formulated the four laws of electromagnetism = Maxwell’s equations.

Electromagnetic induction

Michael Faraday (1791 – 1867) studied electromagnetism and from the knowledge of Hans Christian Oersted and Andre Marie Ampère, who proved that the presence of a magnetic field causes the flow of electric current (directed movement of an electric charge), logically assumed that this analogy also happens in the opposite direction and that the source of electric current may be a magnetic field. The reasoning was the basis of many experiments.


Img. 2 Induction of induced electric current

Electromagnetic induction is a phenomenon in which an induced electromotive voltage and an induced current occur in a conductor due to a change in the time of magnetic induction flux.


The change in magnetic flux induction can occur:

  • by changing the magnetic induction,
  • by changing the capacity of the surface,
  • by changing the angle between the surface normal and the induction lines.


An electromagnet is a type of magnet that converts electrical energy into work = mechanical energy, it exerts a certain force. It is a part of all switching, protection and protection devices. When it comes to frequent switching and small strokes, it is the electromagnet that is suitable for operating these switching machines.


Uses for Electromagnets

The usage of an electromagnet is mainly for the development of smaller forces (it is related to the expansion in contactors) but also for applications in industry or electrical machines. The stroke time of the armature of the electromagnet is small, therefore the size of the work performed is also small. It is not the amount of energy that is significant but its tensile force, which acts during the stroke time.


Static tensile characteristic is the dependence of the tensile force on the stroke of the armature, which expresses the properties of DC or AC electromagnets. Armature tightening time is also an important parameter. When the electromagnet is supplied with direct current, the current does not change in the steady-state, nor the voltage of the coil and one electrical parameter of the excitation winding always stays constant. From the shape of the electromagnets, the size of the air gap and the type of supply = the shape of the static tensile characteristic.

Types of electromagnets

Electromagnets can be divided into:


According to the current:

  • DC electromagnets
  • electromagnets for alternating one-way current,
  • three-phase alternating current electromagnets.


According to the usage

  • motion electromagnets – mechanical force is performed by the movement of the armature (switching devices, brakes, valves…),
  • holding electromagnets – hold ferromagnetic material (clamping, sorting cylindrical, load…),
  • special electromagnets (electromagnetic couplings…).


Principle of operation of electromagnets

The electric current, which is the source of the magnetic field, passes through the excitation coil, where it creates a magnetic voltage that pushes the magnetic flux through the magnetic circuit = a magnetic field with a certain magnetic intensity and a certain magnetic flux is created.


The magnetic flux is directly proportional to the flowing current, which means that the greater the current or the greater the number of turns of the excitation coil, the stronger the magnetic field. A magnetic field acts on the armature of the electromagnet and uses a certain tensile force acting on the armature (ferromagnetic material). If the current of the magnetic field is interrupted and the force is generated, the armature falls to its original position.

Construction of electromagnets

The electromagnet has a simple construction, which consists of an excitation coil, a movable armature and a fixed ferromagnetic core.


Img. 3 Solenoid components, construction of electromagnets

Excitation coil – can have single-layer or multi-layer windings. The number and shape of the air gaps depends on the shape of the magnetic circuit and the coil. The armature located inside the coil may be attracted to the bearing surface or the electromagnet may attract it to the excitation coil. The magnetic circuit is implemented with regard to the economy of operation at acceptable dimensions and weight so that mostly (or completely) the magnetic flux passes through the ferromagnet, which has a very high magnetic conductivity. The individual types of electromagnets (trying to keep the air flow only in the working gap of the electromagnet) have different static tensile characteristics, on the basis of which the correct type of electromagnet for a given application is then selected.


The core and the armature are mostly formed in one-way electromagnets – gaseous ferromagnetic material, in the case of alternating electromagnets – insulated transformer sheets made of ferromagnet (due to the reduction of eddy current losses during alternating magnetization). Cast iron and steel (magnetically hard materials) are not recommended, due to their residual magnetism, which persists even after a power failure.

The work of the electromagnet is affected by swirl currents, which reduce the speed of its application.

Unidirectional electromagnets

The unidirectional electromagnet (DC) consists of a magnetic circuit made of ferromagnetic material (although they have a high conductivity and allow the creation of a strong magnetic field, the transmittance depends on the magnetic induction), a motion armature and an excitation coil which is supplied with direct current.

The core of a DC electromagnet is usually made of solid material.


Benefits of one-way electromagnet:

  • simple construction,
  • quiet operation,
  • in terms of current ratios and their effects on force ratios, dimensions and use of the magnetic circuit,
  • the anchor does not have to be in the end position,
  • the switching density is limited only by the speed of the pull-in and drop-out of the armature.


Disadvantages of one-way electromagnet

  • slower pull,
  • dropping of the armature,
  • lower tensile force compared to AC electromagnets,
  • continuous (maximum) current during the whole application time.


Alternating electromagnets

The excitation coil of the alternating-current electromagnets (AC) is powered by an AC power source. The current is determined by the resistance and the inductance of the coil itself, the inductance depends on the position of the armature.


The switching density is limited by the density of the pull-in and drop-out of the armature and also by the maximum permitted heating. Their force ratios also depend on the degree of saturation of the core.


Benefits of alternating-current electromagnet


  • faster armature tension.



Disadvantages of alternating-current electromagnet

  • magnetic circuit, which consists of electrical sheets,
  • the armature must be placed in the end position to prevent vibrations,
  • humming, due to the vibration of the sheets,
  • when the armature is tightened, shocks occur due to the fact that the tightened current is greater than the rated current.



  1. Adamovic Andrej, Bc., Analýza a optimalizácia vlastností elektromagnetu, Žilinská univerzita v Žiline, Elektrotechnická fakulta
  2. Varga Radovan, Bc., Prípravok pre demonštrovanie účinkov elektromagnetickej indukcie, Technická univerzita v Košiciach, Fakulta elektrotechniky a informatiky

What is a transformer

The history of the transformer began to develop in the 19th century. The principle of the transformer is basically simple and is based on the laws of induction, which were declared in 1833.

A transformer is a non-rotating electrical device that works on the principle of electromagnetic induction (a phenomenon in which an induced electromotive voltage and an induced current occur in a conductor). It is used to convert the electrical energy of a certain voltage into the electrical energy of another, or even the same voltage, if the goal is to galvanically separate two electrical circuits.

The transformer changes the current voltage and voltage ratios in the circuit while maintaining the frequency stays the same. It works only with a voltage that changes over time, means AC or DC pulsating voltage. During the transformation, the performance does not change if we do not consider the losses of the transformer, which consume a small part of the active power in the transformer itself.

In practice, single-phase and three-phase transformers are mostly used.


Fig.1 Basic parts of the transformer – design of the windings (a set of windings, which forms an electrical circuit and is connected to one of the voltages for the transformer or choke coil) of the transformer, the magnetic circuit and the configuration (1) (3).


Transformer composition

Transformer composition

The transformer consists of two or more circuits (windings) and one mutual magnetic circuit (core – a ferromagnetic core is mostly used), which serves as a structural element.

Transformers connected to the electrical distribution network are, in addition to the winding safety, covered with another insulating layer, or are embedded in a suitable potting substance.


The purpose of the transformer is to reduce, increase or make the same voltage and its significance lies in:

  • reducing investment costs,
  • savings over long-distance transmission,
  • safety in electricity consumption.


The well-known discoverer Michael Faraday described the idea of ​​a magnetic field in such a way that the magnetic flows creates the sum of induction lines passing through the investigated space, in our case through the coil cross-section (passive electrical element, which is a real representation of inductance in an electrical circuit). The same flow occurs around the coil, but in the opposite direction. The magnetic induction lines are closed lines and therefore the number passing through the cross-section of the coil returns to the space outside the coil. The size of the magnetic flow can be determined by the number of induction lines inside and outside the coil.


Transformer diagram


Fig.2 Principle of single-phase nuclear transformer


The unit of magnetic flow is the volt second.


Magnetic field


A magnetic field is a physical field in which the field quantities are the intensity of the magnetic field and the density of the magnetic flux. A magnetic field exists at some point if there is a strength that reacts on the moving electric charges or magnets at.


The magnetic field is manifested by a strength acting on iron objects or other magnets. It is located around a permanent magnet or around a conductor through which an electric current flows (where the field of the permanent magnet is actually caused by the movement of charges inside the atoms) and is graphically represented by magnetic field lines (induction lines).


The magnetic field is characterized by magnetic induction, which indicates the number of induction lines per unit area in a relation. The main magnetic field in transformers is concentrated in the iron core because it has a much better magnetic conductivity than air. The induced magnetic flux is proportional to the magnetic conductivity of the circuit and the strength which caused it, which we call the magnetometer power.


The magnetomotive power, also called flow or ampere thread (given in ampermeters) is the sum of currents passing through the excitation, the so-called magnetic circuit window. The magnetic conductivity of a circuit is the ratio of the magnetic flux and the magnetomotive power that causes it. Numerically equal to the size of the magnetic flux induced by the current of one ampere (7).

Types of transformers


According to the shape of the core, transformers are divided into:


Core transformers

Shell transformers

Toroidal transformers


1. Core transformers


This core type of transformers is used for higher performance. The primary and secondary windings are on different columns of the core.

2. Shell transformers


The winding is located on the middle column, which has the largest cross section. The magnetic flux is distributed symmetrically into the connector and the two side columns, which have a half cross section.


The advantage of this configuration is a good distribution of the magnetic flux and small scatterings, simple winding on one coil and a relatively easy fastening of the core bundle. The disadvantage is poor cooling.

3. Toroidal transformers


The base of the toroidal transformer is a circular core made of steel strip in different widths depending on the required final dimensions and power of the transformer. The winding is located around the whole circuit of the toroidal core.


Toroidal transformer


FIG. 3 Powerful toroidal transformer



Construction of small single-phase transformers

A transformer is a device that converts alternating currents and voltages with the same frequency, belongs to non-rotating electrical machines and works on the principle of electromagnetic induction.




According to the current assembly transformers are divided into:

  • Single-phase transformers


A single-phase transformer consists of two coils that share a mild steel core. The primary coil is connected to alternating current, which creates a variable magnetic field in the transformer core.


  • Three-phase transformers


The three-phase transformer has a core with three columns, on one column there can be two or three windings, which are connected to each other by two magnetic connectors. A three-phase transformer is used to transform a three-phase current.


The principle of operation is exactly the same and the construction is very similar to a single-phase transformer. Each phase has its own primary and secondary coil, and they all have one and the same common core, just like a single-phase transformer. The primary as well as the secondary coils are connected to each other either in a star or triangle.


  • Multiphase transformers


A single-coil transformer is also called an autotransformer.


Transformer diagram


FIG. 4 Illustration of a single-phase transformer and scheme of its insertion. It consists of two separate coils – primary and secondary, which are placed on a common mild steel core. An alternating current is transported to the primary coil, which forms a periodic variable field in the core. Due to the variable magnetic field, an electromotive voltage is induced in the coil threads.


A single-phase transformer is used, for example, in radio, television or measuring instruments.


Three-phase transformers with a similar construction are used to transform three-phase current in power engineering.



Cooling methods of Transformers


Powerful transformers must be cooled, as the winding is heated by the passage of an electric current (passive resistance) and the transformer core is also heated by the eddy magnetic currents.


Cooling is usually:


Direct – the cooling medium circulates around the transformer coil.

Indirect – the coil is separated from the medium.


Refrigerant circulation can be natural or forced. In practice, for transformers cooling we use: air (either passive or through fan), oil, water, inert gas (a gas that is not subject to a chemical reaction under the given conditions), solid insulator (line cooling) or other non-flammable liquids (3).

Voltage measurement by transformer


A measuring transformer is an electrical device that transforms a primary current or voltage into a secondary current or voltage that is suitable for supplying measuring or protective devices with the required accuracy.


Their usage is in power engineering, especially when measuring high voltage and high current circuits, where they adapt the ranges of measuring or protective devices.


The purpose of measuring on the transformer is to determine the losses that occur in it, during the operation. From the losses we calculate the efficiencies and the voltage drop from the load. The transformer incurs iron losses, Joule losses in the windings and additional losses.


The usage of a transformer is very advantageous because, in addition to the transformation defined by the number of turns, the measuring transformer also separates the measuring device (connected on the secondary side) from the primary circuit, which is connected to the measuring circuit.



Measuring current and voltage transformers transform large rotating voltages and currents into values ​​suitable for direct measurement using measuring instruments, so we use them to change the ranges of alternating voltmeters. These transformers also separate the measuring instruments from the measured voltage circuits. Voltage measuring transformers are used to increase and decrease ranges. The primary winding is connected parallel to the circuit whose voltage we want to measure. The nominal secondary voltage of the voltage measuring transformers is 100 V, exceptionally 110 V. We connect the measuring device to the secondary side. The primary voltage can reach up to 400 kV.


We divide them according to the purpose of measurement into current and voltage, and their operation is based on the principle of operation of a common transformer.


In a three-phase transformer we identify:


  • measurement of winding resistances
  • measurement of voltage transfer
  • no-load measurement
  • short – circuit measurement (6).





The coil is a passive electrotechnical element, which is a real representation of inductance in an electrical circuit. It consists of an insulated conductor wound (the winding can be single-layer or multi-layer) on a non-conductive carrying frame.


We divide the coils by its construction, shape, number of turns, but the most basic division it’s by its core (without core – air and with core – with magnetic circuit).

Use of coil


A coil that uses the strength effects of the magnetic field of a core is called an electromagnet.


The coil has a triple usage, such as:


  • electromagnet – to create a magnetic field of electric current, the generated magnetic power is used, drawing in the core (electric bell, electric motor, device control…),
  • inductor (inductance carrier) – used to create induction of electric current by magnetic field (LC circuits, radio engineering…),
  • to transform the voltage in the transformers – induction creates an alternating magnetic field in the primary coil, which generates an electric voltage in the second coil of the transformer (secondary winding), the voltage ratio is directly proportional to the ratio of the number of coil threads.


Induction coils


FIG. 5 Different types of coils.



The basic physical value of a coil is inductance, which expresses the amount of magnetic flux induced by a given electric current, and depends on the dimensions of the coil, the number of turns and the permeability of the core.


The unit of inductance is henry.


Choke coil


Coil in the shape of a ring, or cylinder is called a choke coil. Choke coil is a coil with a core (usually made of sheet metal or otroperm strips) and a large value of inductance and its purpose is to filter out signals of higher frequencies in an electrical circuit, to transmit signals of lower frequencies and one-way current with low resistance (4) (5).


Choke coil


FIG. 6 Choke.

Usage of coils


The coils are always intended for a specific targeted product (eg radio receiver, oscillator…) They are not produced in large numbers for different uses.