A magnetic circuit is a fundamental concept in electromagnetism that allows us to understand and analyze the behavior of magnetic fields in different systems. Like an electrical circuit, a magnetic circuit is made up of components that control the flow of magnetic flux, such as magnetic materials and air gaps. By studying magnetic circuits, engineers and scientists can design and optimize devices such as transformers, motors and generators and understand the complex interactions between magnetic fields and materials. In this introductory section we will examine the principles and applications of magnetic circuits, examining their importance in modern technology and their role in shaping our everyday lives.

The magnetic circuit is represented as a closed path derived from the lines of magnetic force, that is, the flux. Such a magnetic circuit is associated with completely different magnetic quantities such as mmf, flow reluctance, permeability, etc.

Consider the simple magnetic circuit shown in Fig. This circle includes an iron core with cross section “a” in m2 and average length “l” in m. A coil with N turns is wound around one of the peripheral edges of the square core, which is excited by a. source. This source passes a current through the coil. This current-carrying coil creates the flux (Ф) that completes its path through the core, as shown in Fig.

## **Magnetic effect of an electric current**

The magnetic effect of an electric current is a fascinating phenomenon that lies at the heart of electromagnetism. It refers to the creation of a magnetic field around a current-carrying conductor. This discovery, first made by Hans Christian Ørsted in 1820, revolutionized our understanding of the relationship between electricity and magnetism. The direction of the magnetic field is determined by the right-hand rule. This states that if you point your right thumb in the direction of the current, the curvature of your fingers will indicate the direction of the magnetic field. This magnetic effect of an electric current is used in numerous technologies. It is the underlying principle behind electric motors, generators, transformers and various other electrical devices. Understanding and exploring this phenomenon paved the way for advances in electricity production, transportation, communications and many other areas of modern life.

This is analogous to a weak circuit in which a voltage source, that is, an electromotive force of E volts, conducts a current I that completes its path through a closed conductor with resistance R. This equivalent circuit is shown in Fig.

Let us derive the relationship between MMF, flow and reluctance.

I = current flowing through the coil.

N = number of revolutions.

Ф = river in Webers.

B = flux density in the core.

µ = Absolute permeability of the magnetic material

μ _{R} = Relative permeability of the magnetic material

The intensity of the magnetic field inside the coil is given by

**H = (NI/l) AT/m**

The flux density is now B = µH

**B = ((µ _{Ó} μ _{R} NI)/ l) Wb/m ^{2}**

**Magnetic field through straight conductor**

Since the cross-sectional area is now “a” m2,

∴ The total flux in the core is

ф = Ba

ф = ((µ _{0} μ _{R} NI a)/l) Wb

that is, ф = (NI)/(l/ µ _{0} μ _{R} A)

ф = mmf / reluctance

ф = F/S

Where,

NI = F (mmf magnetomotive force in AT)

S = (l/µ _{0} μ _{R} a) (Resistance caused by the magnetic path).

This flow expression is very similar to the surface of a circuit current.

I = electromotive force / resistance