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Energy In A Magnetic Cycle

During each magnetic cycle, the energy expended in the specimen is proportional to the area of the closed loop.

Consider a ring of specimen of mean circumference metres, cross-sectional area a metres2 and having N turns of an insulated wire. Let the current flowing through the wire be of I amperes.

Magnetising force, H = NI

or                         I = H l

Let the flux density at this instant be B.

Total flux through the ring, ∅ = B X a
If the current is increased to increase the magnetizing force H and induction density B.
Induced e.m.f. in the coil.

e  = -  Number of turns on coil x rate of change of flux

= - N d  = - Nd(Ba) = - Na dB
        dt              dt               dt

According to Lenz’s law this induced e.m.f. will oppose the flow of current, therefore in order to maintain the current , therefore in order to maintain the current I in the solenoid, the source of supply must have an equal and opposite e.m.f.

Hence applied e.m.f. e = - Na dB

Energy consumed in short time dt = e x I x dt = Na dB X I dt
                                                  = Na dB  X Hl x dt = a l H d B since I = Hl
                                                          dt      N                                      N

          Total energy consumed  =

Now al is the volume of ring and HdB is the area of elementary strip of B-H curve shown in HdB is the total area enclosed by the hysteresis loop.

Energy consumed/cycle = Volume of the ring x area of the loop

Energy consumed per cycle per cubic metre of volme = area of the hysteresis lop

This energy expended in taking a specimen through a magnetic cycle is wasted and since it appears as heat, so it is termed as hysteresis loss.

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