Electrical Engineering ⇒ Topic : Analysis of Magnetic Circuit

ANALYSIS OF MAGNETIC CIRCUITS

The presence of charges in space or in a medium creates an electric field, similarly the flow of current in a conductor sets up a magnetic field. Electric field is represented by electric flux lines, magnetic flux lines are used to describe the magnetic field.The path of the magnetic flux lines is called the magnetic circuit. Just as a flow of current in the electric circuit requires the presence of an electromotive force, so the production of magnetic flux requires the presence of magneto-motive force (m.m.f).We now discuss some properties related to magnetic flux.

(1) Flux density (B) The magnetic flux lines start and end in such a way that they form closed loops. Weber (Wb) is the unit of magnetic flux (Φ). Flux density (B) is the flux per unit area. Tesla (T) or Wb/m² is the unit of flux density.

where B is a quantity called magnetic flux density in teslas, Φ is the total flux in webers and A is the area perpendicular to the lines in m².

(2) Magneto-motive force MMF  A measure of the ability of a coil to produce a flux is called the magneto-motive force. It may be considered as a magnetic pressure, just as emf is considered as an electric pressure. A coil with N turns which is carrying a current of/amperes constitutes a magnetic circuit and produces an mmf of NI ampere turns. The source of flux (Φ) in the magnetic circuit is the mmf. The flux produced in the circuit depends on mmf and the length of the circuit.

(3) Magnetic field strength (H) The magnetic field strength of a circuit is given by the mmf per unit length.

The magnetic flux density (B) and its intensity (field strength) in a medium can be related by the following equation

                      B = μ H

where     μ = μ_oμ_r is the permeability of the medium in Henrys/metre (H/m),

             μ₀ = absolute permeability of free space and is equal to 4π X 10^-7 H/m

and       μ_r = relative permeability of the medium.

Relative permeability is a non-dimensional numeric which indicates the degree to which the medium is a better conductor of magnetic flux as compared to free space. The value μ_r  = 1 for air and non-magnetic materials. It varies from 1,000 to 10,000 for some types of ferro-magnetic materials.

(4) Reluctance (ℜ) It is the property of the medium which opposes the passage of magnetic flux. The magnetic reluctance is analogous to resistance in the electric circuit. Its unit is AT/Wb. Air has a much higher reluctance than does iron or steel. For this reason, magnetic circuits used in electrical machines are designed with very small air gaps

Thus reluctance is a measure of the opposition offered by a magnetic circuit to the setting up of the flux. The reluctance of the magnetic circuit is given by

where l is the length, a is the cross-sectional area of the magnetic circuit and μ is the permeability of the medium.

From the above equations

Analysis of Magnetic Circuit

Consider the magnetic circuit shown in Fig. (a). Suppose the mean length of the magnetic circuit (i.e. length ABCDA) is 1 metres, cross-sectional area of the **core is 'a' m² and relative permeability of core material is μ_r. When current I is passed through the coil, it will set up flux (Φ) in the material.

According to work law, the work done in moving a unit magnetic pole once around the magnetic circuit (i.e. path ABCDA in this case) is equal to the ampere-turns enclosed by the magnetic circuit

The quantity NI which produces the magnetic flux is called the magnetomotive force (m.m.f.) and is measured in ampere-turns. The quantity l/aμ_rμ₀, is called the reluctance of the magnetic circuit. Reluctance is the opposition that the magnetic circuit offers to magnetic flux.

Note that the relationship expressed in eq. (i) has a strong resemblance to Ohm's law of electric circuit (I = E/R). The m.m.f. is analogous to e.m.f. in the electric circuit, reluctance is analogous to resistance and flux is analogous to current. Because of this similarity, eq. (i) is sometimes refened to as Ohm's law of magnetic circuit