## Energy In A Magnetic Cycle

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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

Magnetising force, H =

or I =

N

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

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

dt

Energy consumed in short time dt = e x I x dt = Na

dt

= Na

dt N N

Total energy consumed =

Now a

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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Consider a ring of specimen of mean circumference

*l*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__*l*or I =

__H__*l*N

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.

= - 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__dt

Energy consumed in short time dt = e x I x dt = Na

__dB__X I dtdt

= Na

__dB__X__H__x dt = a*l**l*H d B since*I*=__H__*l*dt N N

Total energy consumed =

Now a

*l*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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