Magnetic Circuit

The lines of force in the case of a magnet do not end on the poles but continue is closed paths within the medium. Similarly, if an electron current is passed through the windings of a ring solenoid, a magnetic flux is set up only within the ring. There is practically no magnetic field in the space outside the ring solenoid. The magnetic flux thus forms a closed circuit within the windings of the solenoid. Such a closed magnetic field associated with the electric current is called magnetic circuit.

Consider a coil of N turns wound uniformly on an iron ring of mean circumferential length l, area of cross-section A and permeability μ. When a current i is passed through the coil, the ring is magnetized. The flux density in the material is
        B = μNi/l
. : the total magnetic flux in the material is given by
        Φ = BA = μNiA/l

or        Φ = NiA/l/μA = M/R_e                                 … (1)

In electric circuit, current = electromotive force/resistance or I = E/R                    … (2)

Following results are obtained by comparing Eqs. (1) and (2).
(i)    Magnetic flux Φ in the magnetic circuit corresponds to the electric current I in the electric circuit.
(ii)    The electromotive force E in the electric circuit corresponds to the electric circuit, the source of electric current is E. In magnetic circuit, the source of magnetic flux is Ni (M). M is called magneto motive force (mmf) and is measured in ampere turns.
(iii)    The resistance R in the electric circuit corresponds to l/μA in the magnetic circuit. The quantity 1/μA is called reluctance of the circuit and is thus given by
R_e =1/μA
It is measured in ampere turns/weber.

. : Eq. (1) becomes, Φ (webers) = mmf (amp. Turns) / Re (amp. Turns / weber)                … (3)

This is called Ohm’s law in magnetism.



Magnetic Circuit of an Electromagnet. The electromagnet consists of a yoke, the limbs, the pole pieces and the air gap.
Let l1 be the effective length and A1 the area of cross – section of the yoke, and let μ1 be the permeability of its material. Then the reluctance of the yoke is l1/u1 A1.  Similarly, the reluctance of each limb is l2 /u2A2 , that of each pole-piece is l3/μ3A3, and that of the air-gap is l4/μ0 A4.

Total reluctance of the magnetic circuit} = l₁/μ₁A₁ + 2l₂/μ₂A2 + 2l₃/ μ₃A₃ + l₄/ μ₀A₄.

Magnetomotive force = M = Ni
            Flux = mmf/total reluctance
            Φ = Ni/ (l₁/μ₁A₁ + 2l₂/μ₂A₂ + 2l₃/ μ₃A₃ + l₄/ μ₀A₄)

. : magneto motive force = M = Ni = Φ (l₁/μ₁A₁ + 2l₂/μ₂A₂ + 2l₃/ μ₃A₃ + l₄/ μ₀A₄)

These calculations are only approximately true because of the leakage of flux in the air gap. However, if the air gap is very small, the leakage of flux is negligible and these equations can be used.



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