Hysteresis Curve

Hysteresis Curve

Vishal kumarUpdated on 02 Jul 2025, 08:05 PM IST

The hysteresis curve, also known as the B-H curve, represents the relationship between magnetic flux density (B) and magnetic field strength (H) in a ferromagnetic material. When a magnetic field is applied to such materials, they exhibit a lagging response in magnetization, creating a looped curve when plotted. This phenomenon, called hysteresis, shows how the material retains some magnetism even after the external magnetic field is removed.

This Story also Contains

  1. Hysteresis
  2. Solved Examples Based on Hysteresis curve
  3. Summary

In real life, hysteresis can be observed in everyday objects like fridge magnets or electromagnets. For example, when you turn off an electromagnet, it doesn't immediately lose its magnetism, illustrating the concept of magnetic memory. Similarly, in mechanical systems like car suspensions, materials can exhibit hysteresis, as they take time to return to their original state after being stressed. Understanding the hysteresis curve is essential in designing efficient transformers, motors, and memory storage devices.

Hysteresis

It is the property of the Lagging of magnetic induction (B) behind magnetic intensity (H) in the case of the ferromagnetic substances.

Hysteresis Curve- This is nothing but the graph of (B Vs H )or (I Vs H) as shown below.

When a non-magnetized material is placed in the long solenoid which is carrying current i as shown in the below figure.

Initially When $i=0$ then $B=0, H=0, I=0$ l.e at Point O .
Now if we increase i, it will result in an increase in B and H and 1 , till saturation point (a) I.e path 1 or Path Oa
Now we decrease H and reduce it to zero by decreasing $\mathrm{i} \Rightarrow \mathrm{I}$.e path 2 or Path ab .
So at point $\mathrm{b}, \mathrm{H}=0$ but $B \neq 0 \Rightarrow B=B_r$ where $\mathrm{B}_{\mathrm{r}}$ is called retentivity or remanence or residual magnetism.
This is happening because, For ferromagnetic materials, by removing the external magnetic field, i.e. $\mathrm{H}=0$, the magnetic moment of some domains remains aligned in the applied direction of the previous magnetising field, resulting in a residual magnetism.

Now we have to remove this residual magnetism of the material or demagnetize the material completely. For this, we will reverse the direction of the current in the solenoid.
So, the process of demagnetizing a material completely (i.e path bc) by applying the magnetizing field in a negative direction is defined as Coercivity.
So At point $c$ we have $B=0$ and $H=H_c$ where $H_c$ is called coercivity.

Coercivity signifies magnetic hardness or softness of substance:
I.,e Magnetic hard substance (steel) ——> High coercivity
Magnetic soft substance (soft iron) ——> Low coercivity.

If, after the magnetization has been reduced to zero, the value of H is further increased in the 'negative' i.e. reversed direction, the material again reaches a state of magnetic saturation, represented by point d.

Next, the current is reduced (curve de) and reversed (curve ea) then The cycle repeats itself till point a.

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Solved Examples Based on Hysteresis curve

Example 1: The use of the study of hysteresis curve for a given material is to estimate the

1) Voltage Loss

2) Hysteresis loss

3) Current loss

4) All of the these

Solution:

Hysteresis

Lagging of magnetic induction (B) behind magnetic intensity (H)

Hysteresis loss is given by the hysteresis curve between I & H

Hence, the answer is the option(2).

Example 2: The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with 1000 turns/cm. The current (in mA) that should be passed in the solenoid to demagnetise the ferromagnet completely is :

1) 1

2) 2

3) 20

4) 40

Solution:

Hysteresis Curve

The graph between B and H is called hysteresis curve

wherein

Magnetic field intensity inside the material will be given by H=ni
and for demagnetization, H=100

so required current

$i=\frac{100}{1000 \text { turns } / \mathrm{cm}}=\frac{100}{10^5 \text { turns } / \mathrm{m}}=1 \mathrm{~mA}$

Hence, the answer is the option(1).

Example 3: The materials suitable for making electromagnets should have

1) high retentivity and high coercivity

2) low retentivity and low coercivity

3) high retentivity and low coercivity

4) low retentivity and high coercivity.

Solution:

Coercivity $(H)$
When $H=H_c, B=0$
i.e. Magnetising fields $(\mathrm{H})$ required to destroy the residual magnetism.

Retentivity -
When $\mathrm{H}=0$ (after having increased from 0 to $\mathrm{H}_{\mathrm{s}}$ ), $\mathrm{B}=\mathrm{B}_{\mathrm{r}}$
$B_r$ - residual magnetism, retentivity

The coercivity of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation.

Materials of high retentivity and low coercivity are suitable for making electromagnets.

Hence the answer is option (2).

Example 4: Hysteresis loops for two magnetic materials A and B are given below :

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

1) A for electric generators and transformers.

2) A for electromagnets and B for electric generators.

3) A for transformers and B for electric generators.

4) B for electromagnets and transformers.

Solution:

Retentivity
When $\mathrm{H}=0$ (after having increases from 0 to $\mathrm{H}_s$ ), $B=B_r$
$B_r$ - residual magnetism, retentivity
Coercivity $(H)$ -
When $H=H_c, B=0$
wherein
i.e Magnetising fields $(\mathrm{H})$ required to destroy the residual magnetism.

Material with higher value of refentivity and coerceivity is good to make permenent magnets i.e A
Graph B is for making electro-magnets and transformers.

Hence the answer is option (4).

Example 5:

The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are :

1) $1.5 \mathrm{~T}, 50 \mathrm{~A} / \mathrm{m}$ and 1.0 T
2) $1.0 \mathrm{~T}, 50 \mathrm{~A} / \mathrm{m}$ and 1.5 T
3) $1.5 \mathrm{~T}, 50 \mathrm{~A} / \mathrm{m}$ and 1.0 T
4) $150 \mathrm{~A} / \mathrm{m}, 1.0 \mathrm{~T}$ and 1.5 T

Solution:

So, from the figure, we can see that the-

x = retentivity, y = coercivity, z = saturation magnetization

So, by matching with the diagram from the question and solution, option (2) is correct.

Summary

The hysteresis curve illustrates the relationship between magnetic flux density (B) and magnetic field strength (H) in ferromagnetic materials. It shows how these materials retain magnetism even after the external magnetic field is removed, demonstrating properties like retentivity (residual magnetism) and coercivity (the field needed to demagnetize). This curve is critical for understanding energy losses, hysteresis losses, and designing electromagnets, transformers, and permanent magnets with appropriate materials based on their magnetic properties.

Frequently Asked Questions (FAQs)

Q: What is the significance of the saturation magnetization in the hysteresis curve?
A:
Saturation magnetization is the maximum induced magnetic moment that can be obtained in a magnetic field. On the hysteresis curve, it's represented by the flat upper and lower portions of the loop, where increasing the applied field no longer increases the magnetization. The saturation magnetization is an intrinsic property of the material and is important in determining the maximum energy product in permanent magnets. It also influences the shape of the entire hysteresis loop and is crucial in applications
Q: How does the hysteresis curve change for nanoscale magnetic materials?
A:
Nanoscale magnetic materials often exhibit significantly different hysteresis behavior compared to their bulk counterparts. As particle size decreases, the hysteresis loop typically becomes narrower, with reduced coercivity and remanence. This is partly due to the increased importance of surface effects and the reduction in the number of magnetic domains. Below a critical size (which depends on the material), particles can become superparamagnetic, showing no hysteresis at room temperature. Understanding these size-dependent effects is crucial in applications like magnetic nanoparticles for medical imaging and therapy.
Q: What is magnetic coercivity, and how is it determined from the hysteresis curve?
A:
Magnetic coercivity, often simply called coercivity, is the intensity of the applied magnetic field required to reduce the magnetization of a material to zero after it has been magnetized to saturation. On the hysteresis curve, it's represented by the intercept on the H-axis (x-axis). There are actually two types of coercivity: the field required to reduce the magnetic flux density (B) to zero is called the B-coercivity, while the field required to reduce the magnetization (M) to zero is the H-coercivity. For most materials, these values are similar, but they can differ significantly in some cases.
Q: What is the relationship between the hysteresis curve and magnetic permeability?
A:
Magnetic permeability, which measures a material's ability to support the formation of a magnetic field within itself, is directly related to the slope of the hysteresis curve. The permeability varies along the curve, with the highest permeability typically occurring in the steepest parts of the curve. The initial permeability is determined by the slope near the origin, while the maximum permeability corresponds to the point of maximum slope on the curve. Materials with high permeability have steeper curves and are more easily magnetized.
Q: How do multi-phase magnetic materials affect the shape of the hysteresis curve?
A:
Multi-phase magnetic materials, which contain two or more distinct magnetic phases, often exhibit complex hysteresis behavior. The resulting hysteresis curve is typically a combination of the curves of the individual phases. This can lead to unusual shapes, such as "wasp-waisted" loops or loops with multiple inflection points. The interaction between phases can result in exchange coupling effects, which may enhance or diminish certain magnetic properties. Understanding these complex curves is crucial in designing materials for specific applications, such as permanent magnets with enhanced energy products.
Q: What is the significance of the initial permeability in relation to the hysteresis curve?
A:
Initial permeability is the slope of the initial magnetization curve at very low field strengths. It represents how easily a material can be magnetized from a demagnetized state. On the hysteresis curve, it's related to the steepness of the curve near the origin. Materials with high initial permeability show a rapid increase in magnetization with small applied fields, which is desirable in applications like magnetic shielding and low-field sensors. The initial permeability is often much higher than the permeability at other points on the hysteresis loop.
Q: How does magnetic annealing affect a material's hysteresis curve?
A:
Magnetic annealing is a process where a material is heated and then cooled in the presence of a magnetic field. This treatment can significantly alter the material's hysteresis curve. It typically results in the development of a preferred magnetization direction, leading to a more square-shaped hysteresis loop with higher remanence in the annealing field direction. This process is used to engineer specific magnetic properties in materials for various applications, such as creating materials with high magnetic permeability.
Q: What is the difference between intrinsic and extrinsic hysteresis loops?
A:
Intrinsic hysteresis loops represent the magnetic behavior of a material without considering the effects of its shape or surrounding space. They plot the intrinsic magnetic induction (B - μ₀H) against the applied field (H). Extrinsic loops, on the other hand, include the effects of the material's shape and the surrounding space, plotting the total magnetic induction (B) against H. The difference is particularly important for materials with high permeability or in shapes that create significant demagnetizing fields.
Q: How does the concept of exchange bias relate to the hysteresis curve?
A:
Exchange bias is a phenomenon observed in systems with interfaces between ferromagnetic and antiferromagnetic materials. It causes a shift in the hysteresis loop along the field axis, effectively increasing the coercivity in one direction while decreasing it in the other. This results in an asymmetric hysteresis curve. Exchange bias is crucial in applications like spin valves and magnetic recording media, where it's used to "pin" the magnetization of one layer in a specific direction.
Q: What is the relationship between a material's crystal structure and its hysteresis curve?
A:
A material's crystal structure strongly influences its hysteresis curve. The crystal structure determines the material's magnetic anisotropy – the preferential directions for magnetization. Materials with high anisotropy, like hexagonal cobalt, tend to have wider hysteresis loops and higher coercivity. Cubic structures, like iron, often have narrower loops. The ease of domain wall movement through the crystal lattice also affects the shape of the curve, with more complex structures generally leading to wider loops due to increased domain wall pinning.