The magnetic line of force is directly proportional to the conductivity of the material. Their SI unit is Henry per meter (H/M or Hm²) or newton per ampere square (N-A²).

The magnetic permeability of the material is directly proportional to the number of lines passing through it. The permeability of the air or vacuum is represented by μ₀ which is equal to 4π×17^-7 H/m. The permeability of air or vacuum is very poor. μ represents the magnetic permeability.

Consider the soft iron ring is placed inside the magnetic field shown above. The most of the magnetic line of force passes through the soft iron ring because the ring provides the easy path to the magnetic lines. This shows that the magnetic permeability of the iron is much more than the air or the permeability of air is very poor.

The permeability of the material is equal to the ratio of the field intensity to the flux density of the material. It is expressed by the formula shown below.

Where, B – magnetic flux density
H – magnetic field intensity

Relative Permeability – The relative permeability of the material is the comparison of the permeability concerning the air or vacuum. The actual permeability of the air or vacuum is very poor as compared to the absolute permeability.

The relative permeability of the material is the ratio of the permeability of any medium to the permeability of air or vacuum. It is expressed as

The relative permeability of the air and the non-magnetic material is one (u₀/u₀ = 1).

The post Magnetic Permeability appeared first on Circuit Globe.

In other words, when the magnetic material is magnetized first in one direction and then in the other direction, completing one cycle of magnetization, it is found that the flux density B lags behind the applied magnetization force H.

There are various types of magnetic materials such as paramagnetic, diamagnetic, ferromagnetic, ferromagnetic and antiferromagnetic materials. Ferromagnetic materials are mainly responsible for the generation of the hysteresis loop.

When the magnetic field in not applied the ferromagnetic material behaves like a paramagnetic material. This means that at the initial stage the dipole of the ferromagnetic material is not aligned, they are randomly placed.

As soon as the magnetic field is applied to the ferromagnetic material, its dipole moments align themselves in one particular direction as shown in the above figure, resulting in a much stronger magnetic field.

Contents:

• Residual Magnetism
• Coercive Force
• Soft Magnetic Material
• Hard Magnetic Material
• Applications of Magnetic Hysteresis

For understanding the phenomenon of the magnetic hysteresis, consider a ring of magnetic material wound uniformly with solenoid. The solenoid is connected to a DC source through a Double pole double throw (D.P.D.T) reversible switch as shown in the figure below:

Initially, the switch is in position 1. By decreasing the value of R the value of the current in the solenoid increases gradually resulting in a gradual increase in field intensity H, the flux density also increases till it reaches the saturation point a and the curve obtained is ‘oa‘. Saturation occurs when on increasing the current, dipole moment or the molecules of the magnet material align itself in one direction.

Now by decreasing the current in the solenoid to zero the magnetizing force is gradually reduced to zero. But the value of flux density will not be zero as it still has the value ‘ob‘ when H=0, so the curve obtained is ‘ab‘ as shown in the figure below. This value ‘ob‘ of flux density is because of the residual magnetism.

Residual Magnetism

The value of the flux density ob retained by the magnetic material is called residual magnetism, and the power of retaining it is known as Retentivity of the material.

Now to demagnetize the magnetic ring, the position of the D.P.D.T reversible switch is changed to position 2 and thus, the direction of flow of the current in the solenoid is reversed resulting in reverse magnetizing force H.

When H is increased in reverse direction, the flux density starts decreasing and becomes zero (B=0) and the curve shown above follows the path bc. The residual magnetism of the material is removed by applying the magnetizing force known as Coercive force in the opposite direction.

Coercive Force

The value of the magnetizing force oc required to wipe out the residual magnetism ob is called Coercive force shown by pink color in the hysteresis curve shown above.

Now to complete the hysteresis loop the magnetizing force H is further increased in the reverse direction till it reaches the saturation point d but in the negative direction, the curve traces the path cd. The value of H is reduced to zero H=0 and the curve obtains the path de, where oe is residual magnetism when the curve is in the negative direction.

The position of the switch is changed to 1 again from position 2 and the current in the solenoid is again increased as done in the magnetization process and due to this H is increased in the positive direction tracing the path as ‘efa’, and finally, the hysteresis loop is complete. In the curve again ‘of’ is the magnetizing force, also known as the Coercive force required to remove the residual magnetism ‘oe’.

Here the total Coercive force required to wipe off the residual magnetism in one complete cycle is denoted by ‘cf’. From the above discussion, it is clear that the flux density B always lags behind the magnetizing force H. Hence the loop ‘abcdefa’ is called the Magnetic Hysteresis loop or Hysteresis Curve.

Magnetic hysteresis results in the dissipation of wasted energy in the form of heat. The energy wasted is proportional to the area of the magnetic hysteresis loop. Mainly there are two types of magnetic material, soft magnetic material, and hard magnetic material.

Soft magnetic material

The soft magnetic material has a narrow magnetic hysteresis loop as shown in the figure below which has a small amount of dissipated energy. They are made up of material like iron, silicon steel, etc.

• It is used in the devices that require alternating magnetic fields.
• It has a low coercivity.
• Low magnetization
• Low retentivity

Hard magnetic material

The Hard magnetic material has a wider hysteresis loop as shown in the figure below and results in a large amount of energy dissipation and the demagnetization process is more difficult to achieve.

• It has high retentivity
• High coercivity
• High saturation

Applications of Magnetic Hysteresis

• Magnetic material having a wider hysteresis loop is used in devices like magnetic tape, hard disk, credit cards, audio recordings as its memory is not easily erased.
• Magnetic materials having a narrow hysteresis loop are used as electromagnets, solenoids, transformers and relays which require minimum energy dissipation.

The post Magnetic Hysteresis appeared first on Circuit Globe.

These circulating currents are called Eddy Currents. They will occur when the conductor experiences a changing magnetic field.

As these currents are not responsible for doing any useful work, and it produces a loss (I²R loss) in the magnetic material known as an Eddy Current Loss. Similar to hysteresis loss, eddy current loss also increases the temperature of the magnetic material.

The hysteresis and the eddy current losses in a magnetic material are also known by the name iron losses or core losses or magnetic losses.

A sectional view of the magnetic core is shown in the figure above. When the changing flux links with the core itself, it induces emf in the core which in turns sets up the circulating current called Eddy Current. And these current in return produces a loss called eddy current loss or (I²R) loss, where I is the value of the current and R is the resistance of the eddy current path.

If the core is made up of solid iron of larger cross-sectional area, the magnitude of I will be very large and hence losses will be high. To reduce the eddy current loss mainly there are two methods.

• By reducing the magnitude of the eddy current.

The magnitude of the current can be reduced by splitting the solid core into thin sheets called laminations, in the plane parallel to the magnetic field. Each lamination is insulated from the other by a thin layer of coating of varnish or oxide film.

By laminating the core, the area of each section is reduced and hence the induced emf also reduces. As the area through which the current is passed is smaller, the resistance of eddy current path increases.

• The eddy current loss is also reduced by using a magnetic material having a higher value of resistivity like silicon steel. Contents:
• Applications of Eddy Currents
• Mathematical Expression for Eddy Current Loss

Applications of Eddy Currents

As you know that by the effect of Eddy Current the heat which is produced is not utilized for any useful work as they are a major source of energy loss in AC machines like transformer, generators, and motors. Therefore, it is known as an Eddy Current Loss. However, there are some uses of this eddy current like in Induction heating.

• In the case of induction heating, an iron shaft is placed as a core of an induction coil. A large amount of heat is produced at the outermost part of the shaft by the eddy current when the high-frequency current is passed through the coil.
  At the centre of the shaft, the amount of heat reduces. This is because the outermost periphery of the shaft offers a low resistance path for the eddy currents. This process is used in automobiles for surface hardening of heavy shafts.
• The effect of eddy current is also used in electrical instruments like in induction type energy meters for providing braking torque
• For providing damping torque in permanent magnet moving coil instruments.
• Eddy current instruments are used for detecting cracks in metal parts.
• Used in trains having eddy currents brakes.

Mathematical Expression for Eddy Current Loss

It is difficult to determine the eddy current loss from the resistance and current values, but by the experiments, the eddy current power loss in a magnetic material is given by the equation shown below:

where,
K_e – co-efficient of eddy current. Its value depends upon the nature of magnetic material
B_m – maximum value of flux density in wb/m²
T – thickness of lamination in meters
F – frequency of reversal of the magnetic field in Hz
V – volume of magnetic material in m³
This is all about Eddy Current loss.

The post Eddy Current Loss appeared first on Circuit Globe.

In other words, the value of the flux density (ob as shown in the figure with the red colour line) retained by the magnetic material is called Residual Magnetism and the power of retaining this magnetism is called Retentivity of the material.

Magnetization occurs by applying the current in one direction, and the flux density is increased until the saturation point (a) is reached. Now to demagnetize the magnetic ring the magnetizing force H is reversed by reversing the direction of flow of the current, as discussed in the article ‘Magnetic hysteresis‘.

When H is increased in the reverse direction, the flux density starts decreasing and become zero and the curve follows the path (bc) as shown in the figure below. This residual magnetism of the magnetic material is removed by applying magnetizing force (oc) called the coercive force in the opposite direction.

This phenomenon of the residual magnetism is widely seen in the transformers, generators, and motors. It is also called as Remanence.

Types of Remanence

Contents:

• Saturation Remanence
• Isothermal Remanence
• Anhysteretic Residual Magnetism
• Reduction of Residual Magnetism

The various types of Remanence are as follows

1. Saturation Remanence
2. Isothermal Remanence

• DC demagnetization residual magnetism
• AC demagnetization residual magnetism

3. Anhysteretic Remanence

Detailed explanation of the various types of remanence is given below:

Saturation Remanence (SIRM)

Saturation Remanence is the total magnetic moment per volume of the sample. It is denoted by Mr, and it is sometimes also called as saturation Isothermal Remanence, denoted by Mrs.

Isothermal Residual Magnetism (IRM)

Generally, by one method of remanence, you cannot identify the residual magnetism of all the magnetic materials as they are different in dimensions, shapes, and properties, thus to measure the residual magnetism of small magnetic particles isothermal Remanence is used. It is denoted by Mr(H).

This method mainly depends on the magnetic field of the material. In this method first the magnetic material is magnetized in an alternating field and after that magnetizing field, H is applied and then removed. It is also called as Initial Remanence.

The Isothermal Remanence is further categorized into two methods

• DC Demagnetization Remanence

This method is also called as DC Demagnetization residual magnetism. It is denoted by Md(H). In this process, the magnet is magnetized in one direction by applying the electric current until it reaches the saturation point, and then applying the current in the opposite direction and removing the magnetic field.

• AC Demagnetization Remanence

As the name itself suggests that AC means the magnet or the magnetic material is magnetized in an (AC) alternating current field and the saturation point is obtained. It is denoted by Ma(H).

. Anhysteretic Residual Magnetism (ARM)

Anhysteretic Remanence is a method in which the magnetic material is placed in a large alternating magnetic field with a small amount of DC bias field. To get remanence, the amplitude of the alternating field is reduced to zero gradually and then the bias DC field is removed from the circuit.

Reduction of  Residual Magnetism

        Residual Magnetism can be reduced by the following methods

•  It can be reduced by 45-50 % by the use of hot-rolled steel material.
• The saturation level of the magnetic material can be decreased by providing higher exciting current.
• The magnetization process should be started with constant force and gradually increasing until the saturation is achieved and then reducing it slowly to demagnetize it further.
• In the process of magnetization and demagnetization of magnetic material the electric force, or the applied current should almost be similar.

The post Residual Magnetism appeared first on Circuit Globe.

When in the magnetic material, magnetisation force is applied, the molecules of the magnetic material are aligned in one particular direction. And when this magnetic force is reversed in the opposite direction, the internal friction of the molecular magnets opposes the reversal of magnetism resulting in Magnetic Hysteresis.

To wipe out or overcome this internal friction (or in other words, known as residual magnetism), a part of the magnetising force is used. This work, done by the magnetising force produces heat; thereby causing wastage of energy in the form of heat is termed as hysteresis loss.

Let us understand this concept by taking an example of electrical machines, as the hysteresis loss occurs mainly where there is a reversal of magnetism, as in the magnetic parts of the electrical machines.

The temperature of the machine is increased as this loss results in the waste of energy, in the form of heat which is an undesirable process for the machines.

Therefore, a suitable magnetic material having a minimum hysteresis loss which has the narrow hysteresis loop is used for making these electrical machinery parts.

Magnitude of Hysteresis Loss

The figure below shows one cycle of magnetisation of the magnetic material.

Consider a strip of small thickness dB on the hysteresis loop as shown in the above

For any value of current I, the corresponding value of flux is,

For the small charge dϕ that are dB x A, the work done will be given as

dW = (ampere-turn) x (change of flux)

The total work done during a complete cycle of magnetisation is obtained by integrating both the side of the above equation 1

Where ʃ HdB is the area of the hysteresis loop

Therefore, W=Al x (area of the hysteresis loop) or

Work done /unit volume (W/m³) = area of the hysteresis loop in Joules.

Now if f is the number of cycles of magnetisation made per second, then Hysteresis loss/m³ = (area of one hysteresis loop) x (f joules/second or Watts)

Hysteresis Loss in the magnetic material per unit volume is expressed as
Where,

P_h – hysteresis loss in watts

Ƞ – hysteresis or Steinmetz’s constant in J/m³, its value depends upon the nature of the magnetic material.

B_max – maximum value of the flux density in the magnetic material in wb/m²

f – number of cycles of magnetisation made per second

V- volume of the magnetic material (part in which magnetic reversal occur) in m³

The post Hysteresis Loss appeared first on Circuit Globe.

The above figure shows a parallel magnetic circuit. In this circuit, a current-carrying coil is wound on the central limb AB. This coil sets up the magnetic flux φ₁ in the central limb of the circuit. The flux φ₁ which is in the upward direction is further divided into two paths namely ADCB and AFEB. The path ADCB carries flux φ₂, and the path AFEB carries flux φ₃. It is clearly seen fro the above circuit that

φ₁ = φ₂ + φ₃

The two magnetic paths ADCB and AFEB form the parallel magnetic circuit, thus, the ampere-turns (ATs) required for this parallel circuit are equal to the ampere-turns (ATs) required for any one of the paths.

As we know, reluctance is

If S₁ = reluctance of path BA will be

S₂ =reluctance of path ADCB will be

S₃ = reluctance of the path AFEB will be

Therefore, the total MMF or the total Ampere turns required in the parallel magnetic circuit will be the sum of all the individual parallel paths.

Total mmf required = mmf required for the path BA +mmf required for the path ADCB + mmf required for the path AFEB

Where φ₁. Φ₂, φ₃ is the flux and S_1, S₂, S₃ are the reluctances of the parallel path BA, ADCB and AFEB respectively.

The post Parallel Magnetic Circuit appeared first on Circuit Globe.

Current I is passed through the solenoid having N number of turns wound on the one section of the circular coil. Φ is the flux, set up in the core of the coil.

a₁, a₂, a₃ are the cross-sectional area of the solenoid.

l₁, l₂, l₃ are the length of the three different coils having different dimension joined together in series.

µr₁, µr₂, µr₃ are the relative permeability of the material of the circular coil.

a_g and are the area and the length of the air gap.

The total reluctance (S) of the magnetic circuit is

Total MMF = φ x S ……..…. (1)

Putting the value of S in equation (1) we get,(As B = φ/a) putting the valve of B in the equation (2) we obtain the following equation for the total MMF

Procedure for the Calculation of the total MMF for the Series Magnetic Circuit

1. The magnetic circuit is divided into a different section or parts.
2. Now determine the value of the flux density (B) of the different sections. As we know B = φ/a where φ is the flux in Weber, and a is the area of cross-section in m²
3. Determine the value of the magnetising force (H) as we know that H = B/µ₀µ_r where B is the flux density in Weber/ m² and µ₀ is absolute permeability and its value is 4πx10^-7, and µ_r is the relative permeability of the material, and its value will be given. If the value of µ_r is not given, then you have to compute the value from the value of H from the B-H curve
4. The value of magnetising force (H) as H_1, H₂, H₃, Hg will be individually multiplied by the length of the different sections that is, l₁, l₂, l₃ and lg respectively.
   
5. Finally, add all the values of Hx l and therefore, the total MMF will be

The value of H for the air gap part will always µ_g = B/µ_0.

B-H Curve

The graph plotted between the flux density (B) and the magnetising force (H) of any material is called B-H Curve or the magnetisation curve.

The shape of the B-H curve is mostly non-linear this means that the relative permeability (µ_r) of the material varies and is not constant. The value of relative permeability mainly depends on the value of flux density.

But for the non-magnetic materials like plastic, rubber, etc. and for the magnetic circuit having an air gap, its value is constant, denoted by (µ₀). Its value is 4πx10^-7 H/m and commonly known as absolute permeability or permeability of free space.

B-H curve for the various material like cast iron, cast steel and sheet steel is shown in the above figure.

The post Series Magnetic Circuit appeared first on Circuit Globe.

Let us understand the phenomenon of Mutual Inductance by considering an example as shown in the above figure.

Two coils namely coil A and coil B are placed nearer to each other. When the switch S is closed, and the current flows in the coil, it sets up the flux φ in the coil A and emf is induced in the coil and if the value of the current is changed by varying the value of the resistance (R), the flux linking with the coil B also changes because of this changing current.

Thus this phenomenon of the linking flux of the coil A with the other coil, B is called Mutual Inductance.

For determining the Mutual Inductance between the two coils, the following expression is used

This expression is used when the magnitude of mutually induced emf in the coil and the rate of change of current in the neighbouring coil is known.

If e_m = 1 volt and dI₁/dt = 1 ampere then putting this value in the equation (1) we get the value of mutual inductance as M=1 Henry

Hence, from the above statement, you can define Mutual Inductance as “the two coils are said to have a mutual inductance of one Henry if an emf of 1 volt is induced in one coil or say primary coil when the current flowing through the other neighbouring coil or secondary coil is changing at the rate of 1 ampere/second”.

Mutual inductance can also be expressed in another way as shown below

Equating equation (2) and (3) you will get

The above expression is used when the flux linkage (N₂φ₁₂) of one coil due to the current (I₁) flowing through the other coil are known.

The value of Mutual Inductance (M) depends upon the following factors

• Number of turns in the secondary or neighboring coil
• Cross-sectional area
• Closeness of the two coils

Mutual Coupling In the Magnetic Circuit

When on a magnetic core, two or more than two coils are wound, the coils are said to be mutually coupled. The current, when passed in any of the coils wound around the magnetic core, produces flux which links all the coils together and also the one in which current is passed. Hence, there will be both self-induced emf and mutual induced emf in each of the coils.

The best example of the mutual inductance is the transformer, which works on the principle of Faraday’s Law of Electromagnetic Induction.

Faraday’s law of electromagnetic induction states that “ the magnitude of voltage is directly proportional to the rate of change of flux.” which is explained in the topic Faraday’s Law of Electromagnetic Induction.

The post Mutual Inductance appeared first on Circuit Globe.

If the current in the coil is increasing, the self-induced emf produced in the coil will oppose the rise of current, that means the direction of the induced emf is opposite to the applied voltage.

If the current in the coil is decreasing, the emf induced in the coil is in such a direction as to oppose the fall of current; this means that the direction of the self-induced emf is same as that of the applied voltage. Self-inductance does not prevent the change of current, but it delays the change of current flowing through it.

This property of the coil only opposes the changing current (alternating current) and does not affect the steady current that is (direct current) when flows through it. The unit of inductance is Henry (H).

Expression For Self Inductance

You can determine the self-inductance of a coil by the following expression

The above expression is used when the magnitude of self-induced emf (e) in the coil and the rate of change of current (dI/dt) is known.

Putting the following values in the above equations as e = 1 V, and dI/dt = 1 A/s then the value of Inductance will be L = 1 H.

Hence, from the above derivation, a statement can be given that a coil is said to have an inductance of 1 Henry if an emf of 1 volt is induced in it when the current flowing through it changes at the rate of 1 Ampere/second.

The expression for Self Inductance can also be given as:

where,
N – number of turns in the coil
Φ – magnetic flux
I – current flowing through the coil

From the above discussion, the following points can be drawn about Self Inductance

• The value of the inductance will be high if the magnetic flux is stronger for the given value of current.
• The value of the Inductance also depends upon the material of the core and the number of turns in the coil or solenoid.
• The higher will be the value of the inductance in Henry, the rate of change of current will be lower.
• 1 Henry is also equal to 1 Weber/ampere

The solenoid has large self-inductance.

The post Self Inductance appeared first on Circuit Globe.

When a current is passed through a solenoid, magnetic flux is produced by it.

Most of the flux is set up in the core of the solenoid and passes through the particular path that is through the air gap and is utilised in the magnetic circuit. This flux is known as Useful flux φ_u.

As practically it is not possible that all the flux in the circuit follows a particularly intended path and sets up in the magnetic core and thus some of the flux also sets up around the coil or surrounds the core of the coil, and is not utilised for any work in the magnetic circuit. This type of flux which is not used for any work is called Leakage Flux and is denoted by φ_l.

Therefore, the total flux Φ produced by the solenoid in the magnetic circuit is the sum of the leakage flux and the useful flux and is given by the equation shown below:

Leakage coefficient

The ratio of the total flux produced to the useful flux set up in the air gap of the magnetic circuit is called a leakage coefficient or leakage factor. It is denoted by (λ).

Fringing

The useful flux when sets up in the air gap, it tends to bulge outward at (b and b’) as shown in above figure, because of this bulging, the effective area of the air gap increases and the flux density of the air gap decreases. This effect is known as Fringing.

Fringing is directly proportional to the length of the air gap that means if the length increases the fringing effect will also be more and vice versa.

The post Leakage Flux And Fringing appeared first on Circuit Globe.