Transformers are vital in industrial and commercial electrical power systems. Here, some facts about magnetic flux in a transformer is explained.

**The necessary requirement for a transformer to work is a time-varying magnetic flux, which in turn, induces emf in the windings. The alternating magnetic flux helps to transfer power from primary to secondary winding. The magnetic core in the transformer is what concentrates the magnetic flux in the windings.**

Further facts on magnetic flux in a transformer are discussed below.

**What is magnetic flux in a transformer?**

**The measure of magnetic field lines passing through a closed surface gives the magnetic flux contained in the surface. It gives an estimate of the net magnetic field crossing a particular area.**

The magnetic flux in a transformer is developed due the varying electric field or current in the primary windings. This is due to mutual inductance or Faraday’s law of electromagnetic induction.

The magnetic lines of force developed due to the alternating current are concentrated by the iron core or any magnetic core in the transformer. The pathway or the connecting link between the primary and secondary windings is this magnetic flux.

**What is the source of magnetic flux in a transformer?**

**A transformer mainly consists of two windings or coils known as primary coil and secondary coil. An alternating current is supplied through the primary windings which produces a magnetic flux due to mutual inductance.**

The working of a transformer is based on the principle of mutual induction where the magnetic flux that is generated as a result of the alternating current or voltage in the primary windings induces an emf in the secondary windings which forms the output.

The varying current passing through the primary coil generates magnetic field lines around it. As the strength of magnetic field increases the soft iron core concentrates the magnetic flux and hence forms a path to the secondary coil.

The varying current linked with the primary winding varies the magnetic field and hence due to this varying magnetic flux, current is induced in the secondary winding.

**What is the importance of magnetic flux in transformer?**

**Magnetic flux is an important factor in the working of a transformer because transformer action is based on the principle of mutual induction. The magnetic flux is the factor that links the primary and secondary coils and the changing magnetic flux is what produces the emf in secondary coil.**

A transformer comprises two coils, primary and secondary coil, and they are not electrically connected by a circuit or a wire. Instead they are only inductively linked. Through the primary coil, an alternating current is supplied. This varying current from minimum to maximum value in each cycle generates a magnetic field in and around the coil.

The transformer also contains a magnetic core, mostly soft iron, around which the primary and secondary coils are wound. This core concentrates the generated magnetic field around the primarily coil and links the secondary coil. The secondary coil remains in the vicinity of changing magnetic flux which induces emf in the coil.

**How to calculate magnetic flux of a transformer?**

The magnetic flux passing through any plane can be accurately described as the number of lines of magnetic induction or field that passes through the same plane.

**In a uniform magnetic field whose magnetic induction intensity is given by B and area of the plane in the direction perpendicular to that of magnetic field is given by S, then the expression for magnetic flux passing through the plane φ is given by the product of B and S.**

**The general expression for magnetic flux is given in terms of the integral of magnetic field on the surface area.**

**integral b.ds where ds is the infinitesimal vector**

For a transformer, often magnetic flux density is used. The expression for maximum magnetic flux density is given by

where,

V = applied rms voltage (in volts)

f = frequency (in Hertz)

N = number of turns on the windings where voltage V is applied

A = magnetic circuit cross-sectional area (in m^{2} )

**What is magnetic core in transformer?**

**Magnetic core serves as pathways for magnetic flux in a transformer. They serve as a link between the primary and secondary windings of the transformer, concentrating the magnetic flux generated by the primary coil and guiding them to the secondary coil. Magnetic cores are materials made of ferromagnetic compounds.**

These magnetic cores have high permeability due to which they can concentrate magnetic field lines and form a pathway to guide the magnetic fields in transformers or other electrical or magnetic devices.

Commonly used materials for magnetic cores are solid iron, carbonyl iron, amorphous steel, silicon steel, laminated magnetic cores, etc. Soft iron proves to be the best magnetic core for use in transformers since their magnetic permeability is high.

**How does magnetic flux change in a transformer?**

In a transformer, magnetic flux is produced as a result of the varying electric field (i.e., alternating current).

**The change in magnetic flux in a transformer happens due to the variations in the current supplied by the AC source. AC source provides an alternating current that varies from negative to positive values in each cycle. These variations produces magnetic field lines around the primary windings.**

As the change in electric field (i.e., as the current value goes from a minima to a maxima) becomes higher, so does the change in magnetic flux.

**What is magnetic flux density of a transformer?**

**Magnetic flux density is an estimate of the amount of the magnetic field concentrated around a magnet or a varying electric current. It is a vector quantity. Magnetic flux density is usually given by **

**where **

**φ**** is magnetic flux (in webers) and **

**A is the area in square meters (m ^{2})**

If the magnetic flux density in cores is improved, then it can reduce the size of the transformers, which would reduce the cost of equipment as well as the cost of materials like silicon-iron, copper, carbon, etc.

**Magnetic Flux In A Transformer:** **Problem**

**Find primary turns of a 444V/222V, 50 Hz single-phase transformer with a core cross-sectional area of 80 cm2, and a maximum flux density of 2 T.**

We know, the equation containing the primary turns and magnetic flux density is given by

First of all, we shall write the given details.

Given, V = 444 V (primary coil input voltage)

f = 50 Hz

A= 80 cm^{2} = [

B_{max }= 2 T

N = unknown

From the equation given at the beginning of the solution, we can rearrange the terms to get N. So

N =125

**Hence the number of turns is 125.**

**Summary**

Hence, this article gives a detailed description of magnetic flux in a transformer, its importance, about the magnetic core and its importance along with a practice problem that will help to comprehend the concepts much better.