# Magnetic Hysteresis

Hysteresis means a lagging behind.  With respect to the magnetic flux in an iron core of an electromagnet, the flux lags the increase, or decreases in magnetizing force.  The hysteresis results from the fact that the magnetic dipoles are not perfectly elastic.  Once aligned by an external magnetizing force, the dipoles do not return exactly to their original positions when the force is removed.  The effect is the same as if the dipoles were forced to move against an internal friction between molecules.  Furthermore, if the magnetizing force is reversed in direction by reversal of the current in an electromagnet the flux produced in the opposite direction lags behind the reversed magnetizing force.

## Hysteresis Loss:

When the magnetizing force reverses thousands or millions of times per second, as with rapidly reversing alternating current, the hysteresis can cause a considerable loss of energy.  A large part of the magnetizing force is then used just to overcome the internal friction of the molecular dipoles.  The work done by the magnetizing force against this internal friction produces heat.  The energy wasted in heat as the molecular dipoles lat the magnetizing force is called hysteresis loss.  For steel and other hard magnetic materials the hysteresis losses are much higher than in soft magnetic materials like iron.

When the magnetizing force varies at a slow rate, the hysteresis losses can be considered negligible.  An example is an electromagnet with direct current that is simply turned on and off, or the magnetizing force of an alternating current that reverses 60 times per second or less.  The faster the magnetizing force changes, however, the greater the hysteresis effect.

## Hysteresis Loop

To show the hysteresis characteristics of a magnetic material, its values of flux density B are plotted for a periodically reversing magnetizing force.  See below figure, this curve is the hysteresis loop of the material.  The larger the area enclosed by the curve, the greater the hysteresis loss.  The hysteresis loop is actually a B-H curve with an ac magnetizing force.

On the vertical axis values of flux density B are indicated.  The units can be gauss or teslas.

The horizontal axis indicates values of field intensity H.  On this axis the units can be oersteds, ampere-turns per meter, ampere-turns, or just magnetizing current, as all factors are constant except I.

Opposite directions of current result in the opposite directions of + H and – H for the field lines.  Similarly, opposite polarities are indicated for flux density as +B or –B.

The current starts from zero at the center, when the material is unmagnetized.  Then positive H values increase to B to saturation at +Bmax  .  Next H decreases to zero, but B drops to the value BR, instead of to zero , because of hysteresis.  When H becomes negative, B drops to zero and continues, to –Bmax, which is saturation in the opposite direction from +Bmax because of the reversed magnetizing current.

Hysteresis Loop for Magnetic Materials.

Then as the –H values decrease, the flux density is reduced to –BR.  Finally, the loop is completed, with positive values of H producing saturation at Bmax again.  The curve does not return to the zero origin at the center because of hysteresis.  As the magnetizing force periodically reverse, the values of flux density are repeated to trace out the hysteresis loop.

The value of either +BR or –BR, which is the flux density remaining after the magnetizing force has been reduced to zero, as the residual induction of a magnetic materials, also called its retentivity.  In figure, the residual induction is 0.6 T, in either the positive or negative directions.

The values of –HC, which equals the magnetizing force that must be applied in the reverse direction to reduce the flux density to zero, is the coercive force of the material.  In figure the coercive force –HC is 300 A· t/m