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## What is a Hysteresis Loop?

A hysteresis loop (also known as a hysteresis curve) is a four-quadrant graph that shows the relationship between the induced magnetic flux density B and the magnetizing force H. It is often referred to as the B-H loop. From hysteresis loops, we can determine a number of magnetic properties about a material. Such as the retentivity, residual magnetism (or residual flux), coercive force, permeability, and the reluctance.

An example hysteresis loop is shown below.

To understand a hysteresis loop, let’s suppose we take a magnetic material to use as a core around which insulated wire is wound.

The coils are connected to a DC supply through a variable resistor to vary the current “I”. We know that current I is directly proportional to the value of magnetizing force (H) as

Where N = number of turns of coil and l is the effective length of the coil. The magnetic flux density of this core is B which is directly proportional to magnetizing force H.

Now, we should be familiar with some important terms related to a **hysteresis loop**.

### Definition of Hysteresis

Hysteresis of a magnetic material is a property by virtue of which the flux density (B) of this material lags behind the magnetizing force (H).

### Definition of Coercive Force

Coercive force is defined as the negative value of magnetizing force (-H) that reduces residual flux density of a material to zero.

### Residual Flux Density

Residual flux density is the certain value of magnetic flux per unit area that remains in the magnetic material without presence of magnetizing force (i.e. H = 0).

### Definition of Retentivity

It is defined as the degree to which a magnetic material gains its magnetism after magnetizing force (H) is reduced to zero.

Now, let us proceed step by step to make a clear idea about **hysteresis loop**.

- Step 1:

When supply current I = 0, so no existence of flux density (B) and magnetizing force (H). The corresponding point is ‘O’ in the graph above. - Step 2:

When current is increased from zero value to a certain value, magnetizing force (H) and flux density (B) both are set up and increased following the path o – a. - Step 3:

For a certain value of current, flux density (B) becomes maximum (B_{max}). The point indicates the magnetic saturation or maximum flux density of this core material. All element of core material get aligned perfectly. Hence H_{max}is marked on H axis. So no change of value of B with further increment of H occurs beyond point ‘a’. - Step 4:

When the value of current is decreased from its value of magnetic flux saturation, H is decreased along with decrement of B not following the previous path rather following the curve a – b. - Step 5:

The point ‘b’ indicates H = 0 for I = 0 with a certain value of B. This lagging of B behind H is called hysteresis. The point ‘b’ explains that after removing magnetizing force (H), magnetism property with little value remains in this magnetic material it is known as residual magnetism (B_{r}). Here o – b is the value of residual flux density due to retentivity of the material. - Step 6:

If the direction of the current I is reversed, the direction of H also gets reversed. The increment of H in reverse direction following path b – c decreases the value of residual magnetism (B_{r}) that gets zero at point ‘c’ with certain negative value of H. This negative value of H is called coercive force (H_{c}) - Step 7:

H is increased more in negative direction further; B gets reverses following path c – d. At point‘d’, again magnetic saturation takes place but in opposite direction with respect to previous case. At point‘d’, B and H get maximum values in reverse direction, i.e. (-B_{m}and -H_{m}). - Step 8:

If we decrease the value of H in this direction, again B decreases following the path de. At point ‘e’, H gets zero-valued, but B is with finite value. The point ‘e’ stands for residual magnetism (-B_{r}) of the magnetic core material in opposite direction with respect to previous case. - Step 9:

If the direction of H again reversed by reversing the current I, then residual magnetism or residual flux density (-B_{r}) again decreases and gets zero at point ‘f’ following the path e – f. Again further increment of H, the value of B increases from zero to its maximum value or saturation level at point a following path f – a.

The path a – b – c – d – e – f – a forms hysteresis loop.

[NB: The shape and the size of the hysteresis loop depend on the nature of the material chosen]

## Significance of Hysteresis Loops

The main advantages of **hysteresis loops** are given below.

- Smaller hysteresis loop area symbolizes less hysteresis loss.
- Hysteresis loop provides the value of retentivity and coercivity of a material. Thus the way to choose perfect material to make permanent magnet, core of machines becomes easier.
- From B-H graph, residual magnetism can be determined and thus choosing of material for electromagnets is easy.