HYSTERESIS

A simple experiment is performed to study the effect of an external magnetic field on ferromagnetic materials. A rod of ferromagnetic material to be studied is kept inside a solenoid as shown in the  following figure. On passing a current through the solenoid, the magnetic field generated induces Magnetic moment inside the rod, the value of which can be measured by an instrument called magnetometer shown symbolically in the figure.
Knowing the volume of the rod, the magnetic moment per unit volume, M, can be evaluated using the formula, B / U0 - M = i(f) = H
where, if = current through unit length of the solenoid which can be found from the current in ammeter and the number of turns per unit length of the solenoid. Thus, from the experimental values of H and M, B can be evaluated and its variation with if can be studied.
The graph of B vs. H can be drawn using the observations. One such representative graph for a ferromagnetic material is shown in the figure on the next page. At the point O in the graph, there is no magnetic field inside the substance. As H ( or if ) is increased, B increases non-linearly becoming maximum at ‘a’ which is the saturation magnetization condition of the rod.
Starting from O, for small values of H, most of the atoms do not respond to the external magnetic field due to their strong bonding with their neighbours.
But, the situation is different for atoms near the domain boundary. Domain boundaries, instead of remaining sharp, start shifting. One of the two adjacent domains increases in size and the other
reduces. On further increasing H, only one domain survives ultimately and the saturation magnetization is acquired near point ‘a’ on the graph. This process is irreversible. On reducing the current, we do not return to the original condition, i.e., when H = 0, we do not get B = 0 and the substance retains some magnetic moment as shown by the curve ab. The value of B when H = 0 is called retentivity or remanence. Now, if the current is increased in the reverse direction, then at point c on the graph, the value of H at which B = 0 is called coercivity. At this point, the magnetic moments of the domains are  again in random directions but with different domain structure. On further increasing the current in the reverse direction, B goes on increasing in the reverse direction and reaches the maximum value at ‘d’ which is the saturation magnetization in the reverse direction. Now on reducing the current, the  Substance follows curve de and again by reversing the current direction and increasing its value, we obtain the curve ea. This process is called hysteresis cycle. The area enclosed by the B-H curve represents the heat energy ( in joule ) lost in the sample per unit volume.