Fundamentals of Electrical Engineering

Magnetic Circuit

Paramjeet Singh Jamwal
M.Tech Scholar
Sant Longowal Institute of Engineering and Technology
Longowal-148106, Punjab, INDIA
  • To derive magnetic flux through a magnetic circuit, a magnetic force (mmf) is necessary. Magneto motive force can be produced when current flows in a coil of one or more turns.
mmf = N.I
H = mmf / l (AT/m)
where l = length of the magnetic flux path (m)
  • Reluctance (ampere/weber) is the property of the magnetic material which opposes the flow of magnetic flux through it.
Reluctance (S) = mmf / Ф = l / µ0.µr.a (For magnetic materials)
Reluctance (S) = mmf / Ф = l / µ0.a (For Non-magnetic materials)
  • Reluctance is inversely proportional to permeance like Resistance is inversely proportional to conductance.
emf = I.R
mmf = Ф.S
  • Ampere turns per unit length of the magnetic flux path for a particular part of the magnetic material can be found out from the standard curve of the materials, plotted as flux density Vs ampere turns per unit length i.e. H (B-H curve of the material), corresponding to the working value of the flux density in that part.
Total ampere turns = B1/µ1.l1 B2/µ2.l2 B3/µ3.l3 + …
  • In Series parallel magnetic circuit
Total ampere turns required = ampere turns required for the common section + ampere turns required for one parallel path
  • In magnetic circuits, the common section generally known as central core or limb. Useful flux Ф, which flows throughout the magnetic circuit. Leakage flux Фl, links partly magnetic circuit and complete its path through air.

Total flux ФT = Ф + Фl



  • The ratio of the total flux produced ФT to the useful flux Ф is called the leakage factor or leakage coefficient. The value of the leakage factor is always greater than unity and varies between 1.15 to 1.25 depending upon the type of magnetic circuit.

leakage factor = ФT / Ф



  • When the flux crosses the air gap it tends to bulge out across the edge of the air gap. This effect of bulging is called fringing. The effect of fringing is to increase the effective gap area,  which in turns reduces the flux density in the air gap.
  • Magnetic Hysteresis – If a magnetic material is magnetized in a strong magnetic field, it retains the considerable portion of magnetism even after removal of the magnetic force. This phenomenon of lagging of magnetization or flux density B behind the magnetizing force H is known as magnetic hysteresis.
  • The magnetic field intensity required to wipe out the residual magnetism Br is called coercive force. Residual magnetism or remanent flux density Br is defined as the magnetic flux density which still remains in magnetic material even when the magnetizing force is completely removed.
  • Hysteresis loop for hard steel is quite wide and hence posses high retentivity power and large coercive force. This type of material is well suited for permanent magnets and not suitable for rapid reversals of magnetisation as in transformers core and choke cores.
  • Steel, silicon alloys have a very narrow hysteresis loop. Since they have  very high permeability and very low hysteresis losses. These materials are more suitable for transformers core and armature cores which are subjected to rapid reversal of magnetization.
  • If the magnetization is carried through a complete cycle, the energy wasted is proportional to the area of hysteresis loop. Hysteresis loss is equal to the energy consumed in magnetizing and demagnetizing a magnetic material.
  • Dr. Charles Steinmetz suggested an empirical formula


Hysteresis loss Ph = ηVf.(Bmax)^1.6
Where – η = Steinmetz’s coffecient
η = 275 (Silicon steel)
η = 500 (Sheet steel)
V= Volume (m3)
f = frequency of magnetic flux reversal


  • When a magnetic material is linked with a variable or alternating flux, an emf is induced in the magnetic material itself according t Faraday’s laws of electromagnetic induction. This induced emf circulates a current in the body of the magnetic materials. These circulating currents are called Eddy  currents and the power losses due to the flow of this current are called eddy current losses.
  • Applications of the eddy current include eddy current braking in induction energy meters and eddy current damping in permanent magnet moving coil instruments.
  • Eddy current loss depends upon the value of induced emf and the resistance offered by the magnetic material to the flow of eddy currents. The resistance can be greatly increased by laminating the material, thereby reducing the magnitude of the eddy current to an appreciable value.
  • Eddy current losses


Pe = k (Bmax)^2.f^2.t^2.V
Where –
k = Eddy current coefficient & its value depends upon the type of magnetic material
t = thickness of material



Basic Electrical Engineering | V N Mittle & Arvind Mittal

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