Namrata Asked:

What is hysteresis? I only know its related to the frequency.

Ans:

Hysterisis mens “Lagging Behind”

Hysteresis phenomena occur in magnetic materials, (as well as in the elastic, electric, and magnetic behavior of materials,) in which a lag occurs between the application and the removal of a field (or force) and its subsequent effect

The lack of retraceability of the magnetization curve is the property called hysteresis

#### Magnetic hysteresis

When an external magnetic field is applied to a ferromagnetic substance, the atomic dipoles align themselves with the external field. Even when the external field is removed, part of the alignment will be retained: the material has become magnetized.

The relationship between magnetic field strength (H)(EXTERNAL) and magnetic flux density (B) (ACQUIRED) is not linear in such materials. If the relationship between the two is plotted for increasing levels of field strength, it will follow a curve up to a point where further increases in magnetic field strength will result in no further change in flux density. This condition is called magnetic saturation.

If the magnetic field is now reduced linearly, the plotted relationship will follow a different curve back towards zero field strength at which point it will be offset from the original curve by an amount called the remanent flux density or remanence (**RETENTIVITY**).

If this relationship is plotted for all strengths of applied magnetic field the result is a sort of S- shaped loop. (See the diagram) The ‘thickness’ of the middle bit of the S describes the amount of hysteresis, related to the **coercivity** of the material.

I am unable to understand why the B value in the BH curve is negative.

Consider an ideal N turn coil wound around a core.

If the voltage applied to the coil is e= Em sin(wt), then the relation between flux in the core and the applied voltage (= induced voltage, if coil has zero resistance) is:

e(t)=Nd(phi(t))/dt, where phi(t) is the total flux in the core (a function of time).

Now, phi(t) = B(t)*A (B = flux densithy in the core, and A is the cross sectional area of the core).

Integrating the voltage, e, from time “0” (zero) to time “t”, one gets:

B(t) = (Em/(w*N*A))*(1-cos(wt)). We see that B(t) is always positive.

So, why is B(t) it shown negative on the B-H curve?