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MAGNETIC CIRCUIT:
The closed loop or path which is followed by magnetic flux is called magnetic circuit.
As electric current flows through electric circuit, flux also flows through magnetic circuit. In the magnetic circuit the flux starts flowing from a point and ends at the same point after completing the path.
Magnetic circuit is made of magnetic materials having high permeability.
Suppose a solenoid having length= l meter,
Cross-section= A meter2,
No. of turn= N turn,
Current = I amp.

Now, field strength, H = NI/l AT/m.
We know, B=µ 0µrH =µ0µrNI/l Wb/m2.
Now flux, ø =BXA Wb.
Or, ø= µ0µrNIA/l Wb.
Or, ø= NI/l/ µ0µrA Wb.
Flux, ø= m.m.f/reluctance.
The flux is directly proportional to the number of turn, N and current, I. That means if no. of turns or current increase, flux increase.
Again flux is inversely proportional to the reluctance. Lower the reluctance, higher the flux.

NOW, WHAT IS M.M.F (MAGNETOMOTIVE FORCE)? AND HOW CALCULATE M.M.F?
It is the property which drives magnetic flux to flow through magnetic circuit. We can say that, it is the magnetic potential same as e.m.f in an electric circuit.
In an electromagnet the total flux is directly proportional to the number of turn of the coil. The total flux is also directly proportional to the value of current, passing through coil. The m.m.f is the product of number of turn and value of current.
M.M.F = No. of turn X Current passing through coil.
= A X T.
The S.I unit of m.m.f is AT(Ampere turn).

RELUCTANCE:
Reluctance is the property which opposes the flow of magnetic flux through a medium. Just like resistance in an electric circuit, which creates an opposition of current, reluctance offered the opposition of flux in magnetic circuit.
The S.I unit of reluctance is AT/Wb.
As, flux, ø = m.m.f/reluctance.
Or, reluctance = m.m.f/ø AT/Wb =1/henry.
Reluctivity: The specific reluctance of a material is called reluctivity as like resistivity.

PERMEANCE:
Permeance is the property of a material for which the magnetic flux conducts. It is the reciprocal of reluctance.
Just like conductance in electric circuit, permeance act in magnetic circuit.
Its S.I unit is Wb/AT or henry.