Magnetic Circuit

Magneto Motive Force (MMF):

    The product of the number of turns and current is known as magneto motive force (mmf), similar to the electromotive force (emf).

MMF = NI ampere-turns 

where mmf - is the magneto motive force in ampere turns

N - is the number of turns wrapped on the core

I - is the current in the coil, in amperes, A.

Reluctance: 

    In the magnetic circuit there is something analogous to electrical resistance, and is called reluctance, (symbol S). The total flux is inversely proportional to the reluctance and so if we denote mmf by ampere turns. we can write    

 φ = NI/S

Where φ is flux , S – reluctance, I - length of the magnetic path in metres.

The unit of reluctance is ampere turns/Wb.

Magnetic flux :

    The magnetic flux in a magnetic circuit is equal to the total number of lines existing on the cross-section of the magnetic core at right angle to the direction of the flux. Its symbol is Ø and the SI unit is weber.

Φ= NI/S

Magnetic field strength :

    This is also known sometimes as field intensity, magnetic intensity or magnetic field, and is represented by the letter H. Its unit is ampere turns per metre.

H= M.M.F/ Length of coil in meters

Flux density (B): 

    The total number of lines of force per square metre of the cross- sectional area of the magnetic core is called flux density, and is represented by the symbol B. Its SI unit (in the MKS system) is tesla (weber per metre square).

B = φ/A Weber/ m2

Permeability: 

    The permeability of a magnetic material is defined as the ratio of flux created in that material to the flux created in air. 

μ = B/H

The permeability of air μ air = unity.
Hysteresis: 

    The name comes from the Greek word `hysteros' meaning `to lag behind'. That is, the state of the flux density is always lagging behind the efforts of the magnetising intensity.

Hysteresis Loop:

    A hysteresis loop shows the relationship between the magnetic flux density B and the magnetizing force H. It is often referred to as the B-H loop.

Looking at the graph, if B is measured for various values of H and if the results are plotted in graphic forms then the graph will show a hysteresis loop.

• The intensity of the magnetism (B)  is increased when the magnetic field (H) is increased from 0 (zero).
• With increasing the magnetic field there is an increase in the value of magnetism and finally reaches point A which is called saturation point where B is constant.
• With a decrease in the value of the magnetic field, there is a decrease in the value of magnetism. But at B and H are equal to zero, substance or material retains some amount of magnetism is called retentivity or residual magnetism.
• When there is a decrease in the magnetic field towards the negative side, magnetism also decreases. At point C the substance is completely demagnetized.
• The force required to remove the retentivity of the material is known as Coercive force (C).
• In the opposite direction, the cycle is continued where the saturation point is D, retentivity point is E and coercive force is F.
• Due to the forward and opposite direction process, the cycle is complete and this cycle is called the hysteresis loop.

Retentivity and Coercivity

    When a ferromagnetic material is magnetized by applying the external magnetizing field, after magnetization if we remove the external magnetizing field, the material will not relax back to its zero magnetization position.

Retentivity

    The amount of magnetization present when the external magnetizing field is removed is known as retentivity.

• It is a material’s ability to retain a certain amount of magnetic property while an external magnetizing field is removed.
• The value of B at point b in the hysteresis loop.

Coercivity

    The amount of reverse(-ve H) external magnetizing field required to completely demagnetize the substance is known as coercivity of substance.

The value of H at point c in the hysteresis loop.

Comparison between magnetic and electric circuits

Magnetic circuit	Electrical circuit
Flux = mmf/ reluctance	Current = emf / resistance
M.M.F. (Ampere-turns)	E.M.F. (Volts)
Flux φ (Webers)	Current I (amperes)
Flux density B (Wb/m2 )	Current density (A/m2)
Reluctance  S=l/A	Resistance R= ρL/A
Permeance = (1/reluctance)	Conductance (= 1/resistance)
Permeability (=1/reluctivity)	Conductivity(=1/resistivity)
Reluctivity	Resistivity

Applications of electromagnets: 

    Electromagnets are used in the manufacture of all types of electrical machines, such as motors, generators, transformers, convertors, some electrical measuring instruments, protective relays, for medical purposes (like removing iron pieces from eyes) and in many other electrical devices like bells, buzzers, circuit-breakers, relays, telegraphic circuits, lifts and other industrial uses.