Magnetic Circuit

A magnetic circuit is nothing but it is a device in which flux flows in a closed path like in a electrical circuit the current flows in a closed loop.

A magnetic circuit is created from magnetic material having high permeability like iron, steel etc.

              Table of Content   
            Mean Core Length
                 Magnetic Flux
        Magnetic Flux Density
       Magnetic Field Intensity
                      MMF
                 Reluctance
                 Permeance
               Leakage Flux  

• Mean Core Length  :

The path taken by the flux has a total length lₑ, which is called Mean core Length.

• Magnetic Flux : 

A magnetic material creates a field around the material. Magnetic flux means the number of line of forces of magnetic field passing through a closed surface, meaning it is a measurement of  the total magnetic field that crossing a specific surface.

Magnetic flux is commonly denoted by Φ(phi)

Formula of magnetic flux , Φ=B.A     

where B= Magnetic field or Magnetic flux density and A= Cross sectional area of the core.

SI unit of magnetic flux is Weber(Wb).

CGS unit of Magnetic flux is Maxwell.

Fundamental unit of magnetic flux is Volt-seconds.

Magnetic flux is generally measured by fluxmeter.

• Magnetic Flux Density :

The flux or line of forces per unit area is termed as magnetic flux density.

Per unit area means per unit current per unit length on a wire

Magnetic flux density is denoted by B.

Formula of magnetic flux density, B=Φ/A

                                                      

                                                      ∴B= Φ/(il)

where l=length of the conductor, i= current flowing through the counductor.

SI unit- weber/m² or Tesla(T)

• Magnetic Field Intensity :

The magnetic field intensity or magnetic field strength is defined by MMF per unit length of the magnetic circuit that means the MMF needed to create a certain flux density(B) within a particular magnetic material per unit length of that magnetic material.

Magnetic field intensity is denoted by H.

 Formula of magnetic flux intensity, H=(Ni)/l

where N= number of turns in magnetizing coil, i= current through the coil, l=length of the coil.

Unit - AT/m

The magnetic field intensity is also known as magnetic field strength or magnetizing force.

N.B:       By using Gauss law of magnetism ,induced flux Φ=∮B.dS 

               

               Magnetic flux density's direction is same as Area Vector.

                and  Area Vector is always perpendicular to Area.

                         So,        Φ=B.A

• Magneto-Motive Force (MMF) :

Like an electrical circuit, emf is the main reason behind the flow of current that whenever there is an emf and there is a closed path, a current will flow in the circuit. Similarly whenever there is an MMF and a closed path available for the flow of flux, the flux will flow inside the magnetic circuit. that means MMF is the driving force which produces the magnetic flux.

As current is responsible of producing flux, so the MMF contains 'i' term.

                                         So,  Magneto-Motive Force(MMF) = Ni

Where N= no of turns of the magnetizing coil and i= current through the coil.

Unit of MMF is Ampere Turns(AT).

As current 'i' is enclosed in a closed path, so according to Ampere-turns law,

                                              MMF, F=∮H.dl          [Assumption: H lies along the magnetic path]  

                                                        F = H*L

              Where H= Magnetic field intensity and L=Total length of the coil or winding.

                                                               As, B=μH

                                                                  ∴ H=B/μ

                                                               ∴ H=Φ/(A*μ)      [∵Φ=B.A]

                                                              So, F = (Φ*L)/(A*μ)

                                                                  ∴F=Φ*R                [R=L/(μ*A)]

                    where Φ denotes Magnetic flux and R denotes Reluctance of the path. 

• Reluctance (R) : 

Magnetic Reluctance for a magnetic circuit is analogous to electrical resistance in the electrical circuit. As resistance is a measure of the opposition to the electrical current. Similarly Reluctance is the opposition offered to the flow of magnetic flux by the magnetic material in a magnetic circuit.

So, Reluctance depends upon the magnetic material that means depends on geometry and composition of the object.

                                                       Reluctance,  R=L/(μ*A)

Where L= length of the magnetic path , A= Cross-section area of the magnetic path  and μ= absolute permeability of the medium. 

Reluctance also define by the ratio of the MMF(F) and the amount of the flux(Φ) produced.

                                     ∴Reluctance, R = (MMF)/Flux

                                                               =(N*i)/Φ

Unit of Reluctance is AT/Wb or Henry⁻¹ .

• Permeance : 

Permeance means the reciprocal of Reluctance that means permeance represents how easily the magnetic flux will be produced in the material. 

                                              ∴Permeance = 1/R

Unit of Permeance is Wb/AT or Henry.

                       

• Leakage Flux :

Leakage flux means a amount of total magnetic flux does not follow the particularly intended path in a magnetic circuit. 

A part of the total magnetic flux flows through the magnetic circuit is called useful magnetic flux. and the magnetic flux which does no completely pass through the magnetic path, but partially passes through the air is call magnetic leakage flux.

                                             Mathematically, Φtotal= Φuseful+Φleakage