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# Magnetic Hysteresis, hysteresis curve, formation, hysteresis losses, hard and soft magnets, practice problems, FAQs

We often use several data storage devices on a daily basis. But have you ever wondered how the material used for making these storage devices are selected. Well they are selected based on their magnetic properties which we are going to study in the topic hysteresis curve.

• Hysteresis Curve
• Formation of Hysteresis curve
• Hysteresis Loss
• Steel and soft iron
• Hard and Soft Magnets
• Properties of material of permanent magnets
• Properties of material of electromagnets
• Practice problems
• FAQs

## Hysteresis curve

The phenomenon in which the value of a physical property lags behind changes in the effect causing it is known as ‘Hysteresis’.

Suppose ‘X’ is a physical property which has some effect on physical property ‘Y’. So, as ‘X’ changes, ‘Y’ also changes but their rate of change is not the same. If the rate of change of ‘Y’ is lesser than or lag behind the rate of change of ‘X’, then the phenomenon is known as ‘Hysteresis’.

Hysteresis is characterised as a lag of magnetic flux density behind the magnetic field strength.

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 magnetising field (𝐻).

## Formation of Hysteresis curve

• When the external magnetic field (𝐻) is acting on a unmagnetized ferromagnetic material, the domains of the material try to align themselves along the direction of 𝐻. Thus, the net magnetic field (𝐵) gradually increases as shown in the 𝑂𝐴 portion of the graph. When the domains are perfectly aligned in the direction of external field, further increase of 𝐻 can’t increase 𝐵 anymore and hence, the material gets saturated. Point 𝐴 denotes the ‘Saturation point’.

• If we gradually decrease the external magnetic field, the net magnetic field decreases. Ideally, this decrement should follow path from 𝐴 to 𝑂 but it follows the path from 𝐴 to 𝐵. The portion 𝑂𝐵 in the graph is known as ‘Retentivity’ of the material.

Retentivity of a material suggests that even if the external magnetic field becomes zero, some internal magnetic field still persists because some of the domains remain oriented in their previous direction.

• Now, if we reverse the direction of the external magnetic field and keep on increasing the intensity of the field, it is seen that at a particular point (𝐶) the material completely loses its magnetic property. The portion 𝑂𝐶 in the graph is known as ‘Coercivity’ of the material. It indicates the required intensity of the magnetic field to completely demagnetise a ferromagnetic material. Larger the coercivity of a material, the material shows larger resistance to getting demagnetised.

• If we gradually increase the external magnetic field in the opposite direction to the initial direction, the net magnetic field increases. Finally, for external field corresponds to point 𝐷, all the domains of the material get aligned along the direction of external field and hence, net magnetic field can’t get increased anymore.

• If we gradually decrease the external magnetic field, the net magnetic field decreases and when the external field becomes zero, the material again retains some magnetic property. The 𝐷𝐸 portion of the graph describes this fact.

• After point 𝐸, if we reverse the direction of external field and keep on increasing the field’s intensity, the material will get demagnetise at point 𝐹 and will get saturated again at point 𝐴.

• The loop 𝐴𝐵𝐶𝐷𝐸𝐹𝐴, formed by this way, is known as the ‘Hysteresis loop’.

In this case, the external field (𝐻) plays the role of “cause” whereas its effect reflects on the net magnetic field (𝐵). Looking at 𝑂𝐵, we can say that although 𝐻 becomes zero at point 𝑂, the net field 𝐵 is not zero at that point rather it becomes zero at later instant. Thus, 𝐵 lags behind 𝐻. Hence, the loop is called ‘Hysteresis loop’. From the whole analysis, we can say that the net magnetic field (𝐵) not only depends on the external magnetic field (𝐻) but also depends on the history processes through which the material has been gone through.

## Hysteresis Loss

Energy lost in the form of heat during a complete cycle of magnetization and demagnetization.

Area of hysteresis loop ∝ Thermal energy developed per unit volume of the material in a hysteresis cycle

## Hard and Soft Magnets

• The ferromagnetic materials which retain magnetisation for a long period of time are called hard magnetic material or hard ferromagnets. Some examples of hard magnetic materials are naturally occurring lodestone and Alnico which is an alloy of iron, aluminium, nickel, cobalt and copper. They are used for permanent magnets. Permanent magnet material should have high retentivity and high coercivity. Memory devices such as audio recording, credit cards and disk drives used in computers use hard magnetic materials. These materials have high coercivity which ensures that memory is not easily erased.
• The ferromagnetic materials which retain magnetisation as long as the external field persists are called soft magnetic materials or soft ferromagnets. Soft ferromagnets are soft iron. Such material is used for making electromagnets. Materials used in electromagnets should have low retentivity and low coercivity.Electric bells, loudspeakers and telephone diaphragms are some of the devices that use electromagnets.

## Properties of material of permanent magnets

• Substances at room temperature, which retain their ferromagnetic property for a long time period.

• Substance should have: High retentivity, high coercivity, high permeability
• Examples: Steel , alnico, cobalt steel and ticonal.
• Uses: In electric clocks, microphones, speakers, generators, motors.

## Properties of material of Electromagnets

• An electromagnet is made from a coil wrapped around a core of soft ferromagnetic material.

• Core material should have: Low retentivity, low coercivity, high permeability.
• Examples: Soft Iron, aluminium.
• Uses: In electric bells, transformer cores, loudspeakers and telephone diaphragms.

## Practice problems

Q 1.  Inside a sample of unmagnetized ferromagnetic material the variation of flux density varies with the magnetic flux density in which the sample is kept is illustrated in the figure. For the sample to be suitable for making a permanent magnet.

a. 𝑂𝑅 should be small, 𝑂𝑄 should be large.
b. Both 𝑂𝑄 and 𝑂𝑅 should both be large.
c. 𝑂𝑄 should be small and 𝑂𝑅 should be large.
d. Both 𝑂𝑄 and 𝑂𝑅 should both be small.

A. (b)

Permanent magnets have high retentivity and high coercivity. Therefore both 𝑂𝑄 and 𝑂𝑅 should be large

Q. Which material is better for use in a coil of the generator or the core of a transformer.

a. Soft iron
b. Mild steel
c. Stainless steel
d. Hard iron

A.

Soft iron has low coercivity and low retentivity.

The core of a transformer undergoes rapid cycles of magnetization and demagnetization, during its working. If a material has larger retentivity and coercivity, then a large amount of energy will be lost to demagnetize the substance, in each and every cycle.

To minimise this loss, the material must have low retentivity and coercivity.

Q 3. The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with. Find the current that should be passed in the solenoid to demagnetize a ferromagnet completely.

A. We know that the intensity of magnetisation required to demagnetise the magnet is equal to the coercivity.

The y-axis component must be zero, for the entire ferromagnetic material to demagnetize, i.e.,

Clearly, at this point, the value of coercivity, is

Putting this value of in equation (1), we get:

So, the current that should be passed in the solenoid to demagnetise a ferromagnet completely is .

Q 4. An iron rod is subjected to cycles of magnetisation at the rate of . The density of the rod is and the specific heat is . Find the rise in temperature per minute(the nearest integer), if the area enclosed by the B-H loop corresponds to an energy of .

(Assume there is no radiation losses)

A.

Given:

Frequency,

Density, ,

Specific heat,

Area enclosed by the B-H loop is called equivalent energy loss per unit volume. so,

Energy loss per unit time,

As, the loss of energy in the process of magnetising is equivalent to the amount of heat generated in the rod.

So, If is the rise in temperature and of the rod then, using energy conservation, we can write,

that rises in one second.

Now, rise in temperature per unit minutes will be,

## FAQs

Q. What is the correct measure of magnetic hardness of a material?
A. Coercivity is the resistance of a magnetic material to changes in its magnetization. It is equivalent to the field intensity necessary to demagnetize the fully magnetised material. Therefore, coercivity is the correct measure of magnetic hardness of a material.

Q. What are the properties that material of permanent magnet must possess?
A. Material required for making permanent magnets should retain magnetic properties permanently and should not get demagnetized easily. Hence, in order to make a good permanent magnet, the material should have a high value of retentivity and a high value of coercivity.

Q. How can hysteresis be reduced?
A. Hysteresis losses can be reduced by selecting materials with the smallest hysteresis loop area. Materials like silicon steel or high-grade steel are used with a small hysteresis loop area to make the core of the electrical machines.

Q. What are the applications of hysteresis loop?
A.  The hysteresis loop of different materials is used to compare retentivity, coercivity and energy loss. Therefore, a suitable material is selected for making electromagnets, transformers, permanent magnets, generators etc.

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