13 Jul 2026

B-H Loop and Hysteresis Loss of a Ferromagnetic Core

practical pg-iv cmp magnetism hysteresis bh-loop

Experimental arrangement

The iron sample is magnetised by the primary winding while the secondary signal is integrated to obtain the B-H loop.

Aim

To plot the B-H curve of an iron sample and determine its hysteresis energy loss.

Apparatus

Iron ring or transformer core, primary and secondary coils, CRO, integrator circuits, AC supply, and voltmeter.

Theory

The primary winding produces the magnetising field

\[H=\frac{NI}{l},\]

where $N$ is the number of turns, $I$ is the current, and $l$ is the magnetic path length. The secondary winding produces an induced voltage proportional to the changing flux,

\[e_s=-N_sA\frac{dB}{dt}.\]

After integration, this voltage gives the magnetic induction $B$. As the current is increased and reversed, domain walls move and magnetic moments rotate, so the material does not return along the same path. The area of the resulting B-H loop represents hysteresis energy loss per unit volume per cycle:

\[W_h=\oint H\,dB.\]

Observations

$H$ (A m$^{-1}$)	$B$ (T) on increasing field	$B$ (T) on decreasing field
0	0.00	0.62
100	0.48	0.73
200	0.86	0.91
300	1.10	1.08
400	1.25	1.20

Retentivity: $B_r=0.62\,\text{T}$; coercivity: $H_c=95\,\text{A m}^{-1}$.

Graph

Measured B-H loop of the iron sample.

Calculation

At zero applied field on the decreasing branch, the specimen retains $B_r=0.62$ T. The field required to bring the induction to zero is read from the horizontal axis as $H_c=95$ A m$^{-1}$. The area enclosed by the loop is obtained from the plotted points; for this trial curve it is approximately

\[W_h=\oint H\,dB\approx0.18\,\text{J m}^{-3}\text{ cycle}^{-1}.\]

Thus a larger loop area would mean greater energy loss in repeated magnetisation.

Result

The iron sample shows a closed hysteresis loop with

\[\boxed{B_r=0.62\,\text{T}},\qquad \boxed{H_c=95\,\text{A m}^{-1}}.\]

The loop area gives the hysteresis energy loss per unit volume per cycle.

Precautions

1. Demagnetise the core before beginning.
2. Avoid saturation of the CRO input.
3. Use a calibrated integrator.
4. Keep the frequency constant while comparing losses.

Viva Questions

1. What is retentivity? It is the residual magnetisation when the applied field is reduced to zero.
2. What is coercivity? It is the reverse field required to reduce the residual induction to zero.
3. What does the loop area represent? Energy dissipated per unit volume per cycle.

Maxima Code

Download the PG-IV B-H loop calculation.