Electrical

# Introduction to Magnetic Field and Magnetic Flux

## Magnet

Introduction to Magnetic Field and Magnetic Flux- Any substance which has a capacity to attract or pull iron or steel pieces towards it is called a magnet. In other words, an iron bar, which can attract other iron pieces toward it, is known as a magnet.

### Magnetism

The capacity of a magnet to attract iron or steel towards it is called magnetism. In other words, the capacity of a magnet, through which it attracts iron-made items towards it, is known as its magnetism.

## Types of Magnets

Magnets are usually found in the following two types;

### Natural Magnet

Magnets that are found naturally in the form of stones are called natural magnets. In the eleventh century AD, a special type of stone was discovered at a Central Asian location Magnesia, which possessed magnetic features. In ancient times, they were used for shipping purposes. Our earth itself is a gigantic magnet.

### Artificial Magnet

Magnets, which are manufactured under a specific principle (electricity or abrasion) through some other magnet, are known as artificial magnets. In other words, magnets formed through any other magnetic objects, are known as artificial magnets, e.g., Bar Magnet, Electro Magnet, etc. The magnetic power of these magnets can be increased or decreased, e.g., iron, nickel, cobalt, etc. Some of the artificial magnets are permanent while some others tend to be of a temporary type. Temporary magnets are those, the magnetism of which continues so long as they are provided supply. As soon as supply cuts off, their magnetism also ceases.

## Properties of Magnet

A magnet consists of the following characteristics.

i). It attracts iron and iron–made objects towards it.

ii). The power to attract objects is maximum on magnet ends

iii). If a magnet is hanged freely, it always maintains a North-South direction.

iv). It always has two poles. That pole of a magnet, which is southward, is called the south pole, and the pole which is Northwards, is known as its North pole.

v). If a magnet is broken into several pieces, then every piece tends to be a magnet, properly having two poles.

vi). Two similar magnetic poles repel each other while opposing poles attract each other.

vii). A magnet’s lines of force always intrude into the South pole from the North pole.

viii). Magnetic lines never intersect each other.

## Magnetic Field

Any space in which a magnetic effect can be detected constitutes a magnetic field. Remember, that a magnetic field consists of such lines of force, which enter the South pole (S) from its North pole (N), and moves back to the North pole passing through the magnetic material. In figure 4.1, a few lines found around a magnetic bar have been depicted for an easy understanding. The power of lines of force tends to be high near the magnet and low at a distance from the magnet. It has to be remembered that these lines never intersect each other, and always adopt parallel paths. Moreover, these lines are not visible.

Figure 4.1 – Magnetic lines of force around a bar magnet

## Magnetic Poles

When an enduring magnet is hung in such a way, that it can move freely on its horizontal plane, as has been illustrated in fig. 4.2, this magnet always assumes a North-South direction with respect to earth (that’s no matter whatever the direction of a magnet is set through rotating, it always twists its direction towards North and South). The end of a magnet, which assumes the Northern direction, is called the North Pole, whereas the end, which adopts the southern direction, is called the South Pole. The north pole is also indicated by (N) whereas the South pole is represented by (S).

Figure 4.2 – A suspended permanent magnet

### Attraction and Repulsion of Magnetic Poles

When two unlike poles of any two permanent magnets are brought closer to each other, an attractive force generates between them as a result of their individual magnetic fields. This has been shown in figure 4.3 (a), and when two alike poles of any magnet are brought closer to each other, these poles tend to repel each other (that’s a force generated between these two, owing to which they repulse each other). This has been illustrated in figure 4.3 (b).

Figure 4.3 – magnetic attraction and repulsion

## Magnetic Flux

The total number of lines of forces or magnetic lines existing on a magnetic field is known as magnetic flux. In other words, the total number of magnetic lines (which enter the South pole from the North pole) around a magnet, is known as magnetic flux. It is represented by Φ. In other words, the total number of lines threading through the field is called the magnetic flux, symbol Φ.

These types of magnetic lines are invisible, that’s they do not have any physical existence, and they can be sensed only through a magnetic needle (compass needle). In the MKS system, flux is represented by the electrical magnetic effect instead of magnetic lines. Its unit is weber, which is equal to 108 magnetic lines or Maxwell. A weber is that number of magnetic lines, under which one-volt e.m.f produces by revolving the conductor by one second.

1 weber = 1 volt x 1 second

### Characteristics of Lines of Magnetic Flux

Even though magnetic lines have no physical presence, it has the following characteristics;

(i). Magnetic lines start from the Northern pole and finish on the southern pole.

(ii). Every line of a magnetic flux forms a close loop

(iii). The lines of a magnetic flux always thread parallel and they never intersect each other.

(iv). These lines are invisible.

(v). The magnetic flux lines always attempt to shorten themselves in size.

(vi). If these lines, which tend to be parallel to each other, have the same direction, then they repel each other. See fig. 4.4.

Figure 4.4 – magnetic fields due to parallel current-carrying conductors

(vii). Every point of magnetic lines of force indicates the intensity of a magnetic field. It has a direction similar to that of the tangent on these lines of force on this point.

(viii). Magnetic lines always form semi-circular lines.

(ix). Magnetic lines try to shrink just similar to flexible threads

### Flux Density

(i). The number of magnetic lines which pass through a unit area of a unit magnetic bar, is called flux density. It is denoted by B.

(ii). The number of lines of force that pass through a unit area of the vertical surface, is known as magnetic induction or flux density.

(iii). The flux per square meter at right – angles to the magnetic field is called the magnetic flux density or magnetic induction.

(iv). The per square meter flux existing on an absolute angle of a magnetic field, is called flux density.

(v). The flux density is the amount of flux per unit area in the magnetic field.

If the cross-section area of a magnetic field is A and the quantity of flux be Φ weber, then the value of flux density will be as follows;

B = Φ / A Weber / Meter2

The unit of flux density is weber per square meter or Tesla.

### Magneto – Motive Force (M.M.F)

When electricity flows through a coil, a magnetic force generates, which operates magnetic lines of flux. It is called magneto–motive force. In other words, pressure as a result of which magnetic flux switches from the North pole to the South pole, is called magneto motive force. Or it is a force, which operates a flux within a magnetic circuit (similar to electromotive force (E.M.F) which runs electrons in an electric circuit), is called magneto motive force. The pressure required to establish magnetic flux in a ferromagnetic material (material having permeabilities hundreds and thousands of times greater than that of free space). It is measured in ampere-turns.

### Magnetizing Force or Magnetic Field Strength

The m.m.f per meter length of the flux is termed the magnetizing force or magnetic field strength. Symbol H

In other words, the force of a unit length magnetic field of any conductor or air core coil is called its magnetizing force. The power of a magnetizing field for a single conductor is as follows;

H = I / ℓ amperes per meter or N / wb or oersted

Here, ℓ means the length of the flux path in meters. Remember that H is measured as flux path’s amperes per meter instead of the current path.

A round flux path having a radius r meters, and an “I” amperes current flowing through it, the magnetizing force will be as follows;

H = I / ℓ = I / 2 amperes per meter

Thus, Ħ is inversely related i.e., the magnetic effect reduces as the distance from the conductor increases.

If I amperes current flows through coil consisting of N turns, as has been shown in figure 4.5, then a magnetizing force equivalent to total current linked to the magnetic circuit, produces, that’s IN Turns. If a magnetic circuit is perfectly identical with respect to the cross-section area and structure, then e.m.f of one meter of the circuit is called magnetic field strength (H).

Figure 4.5; A toroid

Thus, if the average length of any magnetic circuit is ℓ meters, then;

H = IN ℓ amperes / meters

In other words, the strength of a magnetic field found on any point of a magnetic field equals the force generated by the N pole of one weber on that point, i.e.,

H = Force Experienced by N Pole of 1 Weber / Distance

Remember, that a power of a magnetic field (H) is also called magnetic intensity.

Susceptibility

The intensity of magnetization (I) and the ratio of magnetizing force (Ħ) are called susceptibility. It is denoted by K, i.e.,

K = I / H Henry per meter

### Retentivity

That feature of any material, under which that material retains its magneticity after separating from the magnetizing force, is called retentivity of that material, e.g., when a coil made from a specialized material, is connected to the supply, it turns into a magnet. When supply is turned off, the magneticity of the coil either abolishes completely or a little magneticity remains in the coil for some time, which depends on the coil material.

## Classification of Magnetic Materials

There are normally two types of materials, i.e., a magnetic material and non-magnetic material. Magnetic materials are those, which can be magnetized. For example, steel, iron, nickel, etc. Non-magnetic materials are those which cannot be magnetized, e.g., wood, paper, plastic, rubber, etc.

Magnetic materials can further be divided into three types;

1. Diamagnetic
2. Paramagnetic
3. Ferromagnetic

### Diamagnetic Materials

Materials, having atoms that do not have any resultant magnetic field (or that do not have permanent magnetic motion), are known as diamagnetic materials. These materials always generate magneticity opposite to the applied magnetic field. Therefore, they become a cause of a weakening of the magneticity inside them. The magneticity of these materials does not depend on temperature, e.g., copper, gold, antimony, zinc, mercury, silver, etc. Materials constituted of atoms having zero magnetic moments that are weakly repelled by a magnet, are called diamagnetic or non-magnetic materials.

We know that atoms of every substance consist of electrons. These electrons apart from revolving around their nucleus, also rotate around their axis. A magnetic field builds up as a result of the rotation of electrons around the nucleus, as well as rotation around their axis. As an atom consists of several electrons, therefore, every electron forms a separate magnetic field. As an atom consists of several electrons, therefore, every electron forms a separate field. The ratio and movement of different fields formed as a result of various electrons in an atom are such that these fields either sum up together or tend to cancel each other. If the magnetic fields formed as a result of the motion of different electrons of an atom, add up together, a resultant field builds up. As a result of which, that atom turns into a tiny magnet. It is known as a magnetic dipole.

If such magnetic fields form as a result of the orbital or pivotal motion of electrons (pivotal movement is also called a spin movement), that they cancel each other, then no resultant magnetic field will form up on the atom (that’s the atom’s resultant magnetic field becomes zero). Materials, atoms that have no resultant magnetic electric field, are known as diamagnetic materials. The permeability of these materials tends to be less than 1. These materials magnetize in a very weak manner, and the direction of their resultant magneticity tends to be opposite to the direction of the applied magnetic field.

The materials have a permeability slightly less than that of free space and offer a slight opposition to magnetic lines of force are called diamagnetic materials, e.g., copper, silver, hydrogen, etc.

### Paramagnetic Materials

A specific magnetic field generates as a result of the orbital motion of an electron, and a magnetic field also builds up as a result of axis motion or spin motion of electrons. If the direction of both the fields is such that they support each other, then a resultant magnetic field forms on the atom. Substances or materials comprising the types of materials, which have a magnetic field, are known as paramagnetic materials. For example, aluminum, platinum, chromium, manganese, etc. The permeability of such materials turns out to be slightly higher than 1, and these materials are weakly magnetized in the direction of a magnetizing field. Paramagnetic materials are susceptible to being attracted by a magnet towards it. The materials, that have a permeability just slightly greater than that of free space and are very slightly magnetized are called paramagnetic materials, e.g., platinum, aluminum, oxygen, etc.

### Ferromagnetic Materials

These are materials consisting of atoms that not only generate a magnetic field, but certain atoms also establish strong magnetic effects through their mutual support, e.g., iron, cobalt, nickel, etc. In other words, some of the solid bodies or materials are such that they can retain quite a large quantity of magneticity up to a certain temperature, even if the force forming a magnetic field is removed, later on, such materials are called ferromagnetic materials. The permeability of such materials tends to be higher than 1, and their working depends on the magnetic field strength. That’s the reason, these materials are vastly used in electrical and electronics engineering. Many alloys of iron, nickel, cobalt, and manganese are ferromagnetic materials. Iron is the most distinctive one within ferromagnetic materials. The materials which can be magnetized very strongly (like iron) are called ferromagnetic materials, e.g., iron, cobalt, or nickel)

Relation Between B – H Curve

Magnetizing force H at any point of a magnetic field expressed as amperes per meter is the force, which apart from retention of magnetic flux, also produces a specific flux density value B at this point, therefore, H is known as a cause, whereas B is termed as effect of that cause. If this relation between B and H is represented by a graph, it is known as a B – H curve.

At ant point on a non- magnetic material (e.g., air, or space, etc.), the value of B tends to be directly proportional to H, that’s the graph of B and H turns out to be a straight line. Because;

B = 𝜇 0 H or 𝜇 0 = B / H

Here, 𝜇 0 refers to the permeability of any free space or non – magnetic material, which is also known as magnetic space constant. Its value under the MKS system is 4 𝜋 x 10-7. Thus, magnetic field strength of non – magnetic materials is as below;

H = B / 𝜇0 = B / 4 𝜋 x 10 -7

If a non- magnetic core (a similar core has been shown in figure 4.5) is converted to an iron core, a huge increase occurs in flux through a given e.m.f. The ratio of flux density produced in any material and the flux density ratio in any non-magnetic material (space or vacuum) is known as relative permeability, provided that the circuit’s magnetic field strength remains constant. It is denoted by 𝜇1. Therefore, the B-H curve of any non-magnetic material (e.g., iron) does not tend to be a straight line, rather it is slightly tilted or crooked, and a stage arrives, when this curve assumes a horizontal shape. In such a situation, we say that iron has been saturated.

Remember that the value of 𝜇 г for air tends to be 1. The relative permeability of a ferromagnetic material on different values of H tends to be very high. Therefore, a material having relative permeability value of 𝜇 г, will have flux density as below;

B = 𝜇r 𝜇0 H

B-H curve is also known as hysteresis curve.

## Magnetic Hysteresis

The lagging of flux density B behind the magnetizing field H is called magnetic hysteresis. In other words, the property of any magnetic material, as a result of which dissipation of energy or consumption of energy occurs owing to the inversion of magnetic direction, is known as magnetic hysteresis.

Suppose that there is a non-magnetized iron bar AB, and it is going to be magnetized by placing it inside a solenoid field. This has been illustrated in figure 4.6.

As a consequence of solenoid, H field generates (H = NI / l), which is known as magnetizing force. In order to reduce or increase the value of H, the value of current flowing within the coil is either raised or lowered. Let us assume that the value of H has been gradually increased from zero and brought to a specific maximum value, and flux density values have also been noted alongside an increase in the value of H. Now, if the relation developing between the different values of B and H is denoted by means of a graph, it is reflected in the shape of a curve, which has been represented by a curve OA in figure 4.7. The material becomes saturated by that time as a result of magneticity. When the value of H equals OM, i.e., H = OM, the flux density of material  B also spikes to its maximum value at that time (i.e., B max).

Now, if the value of “H” is decreased step by step (by means of bringing down the solenoid current slowly in steps), then the value of flux density B will not decline so rapidly from A towards O. Rather, its value will decline extremely slowly from A towards C. When the value of H comes down to zero, then instead of becoming zero, B assumes a specific value (Br), which is equal to OC, (i.e., Br = OC). It means that iron bar does not get completely de-magnetized, even if the magnetizing force H has been completely eliminated, rather a certain value of the magneticity still remains available in it. This value of B (which is equal to OC), reflects remanence or retentivity of the material, or this value is called residual flux density Br of this material.

Figure 4.7

To de-magnetize the iron bar, we change its direction of the magnetizing force H. When the direction of H is changed (which is done through changing the direction of current in a solenoid tube), then the value of flux density becomes zero at point D. The value of H which is required to completely remove or abolish the residual magnetism, is known as coercive force (Hc).

Now, if H’s value is increased further in a reverse or opposite direction after the magnetization has become zero, then iron bar again reaches a state of magnetic saturation (saturation refers to that state of an iron bar, after reaching which retention of further magneticity is not possible), which is represented by point L. By equating H back to the negative saturation level OL, and bringing it up to the positive saturation level OM, we get the curve EFGA. If we restart from G once again, then a constant or same curve GACDEFG is obtained again.

It has become clear from the afore-mentioned discussion that B always lags behind H, that’s values of both cannot be zero at a time. The lagging in this way from H is generally termed as hysteresis. The closed loop ACDEFQA (which is obtained when a whole cycle of magneticity passes through an iron bar) is known as hysteresis loop. Remember that the shape of a hysteresis loop depends on the nature of magnetic material. The larger the loop of any material formed (or the larger the loop area) the larger would be the energy loss in that material (in the form of heat). Therefore, an alloy steel has a thin or narrow loop as compared to a hard steel. That’s the reason, an alloy steel is mostly preferred in manufacturing the cores of transformers, electrical motors, and dynamos, etc., so that AD current and hysteresis loss could be minimal.

Figure 4.8

In the figure 4.8b

loop areas of different materials have been shown. it should be remembered here that the higher will be loss of energy, the larger the size of a loop (That’s as a result of hysteresis, energy loss occurs in the form of heat, and this dissipation of energy is directly proportional to the area of a loop).

## Magnetic Circuit

It may be defined as “The route or path which is followed by magnetic flux is called magnetic circuit or the path of the flux round any current carrying circuit, is called a magnetic circuit.

Ampere Turns (AT)

This is the unit of magneto motive force (m. m. f). An ampere turn (AT) is obtained from the product of the number of turns existing in a magnetic circuit and the current carrying through these turns.

### Reluctance

That property of any material, which oppose the creation of magnetic flux in it, is called reluctance. It is denoted by S. In other words, it is the quantity of opposition being faced by a flux inside a magnetic circuit, which is identical to the resistance of the electric circuit. Its unit is ampere – turns per weber (AT / W).

S= / 𝜇 A = ℓ / 𝜇0 𝜇r A

Here, means average length of the flux path, A means uniform cross – sectional area of magnetic circuit, 𝜇0 means absolute permeability, and 𝜇r means relative permeability of the material.

Thus, reluctance is directly proportional to the length of flux path, whereas inversely proportional to the cross-sectional area and permeability. Reluctance can also be defined in the following words;

The ratio of the magneto – motive force to the flux is called reluctance of the magnetic circuit.

S = m.m.f / Փ

As units of m.m.f and flux are ampere – turns and weber respectively, therefore, unit of reluctance is called ampere turns per weber (AT / W).

### Permeance

The inverse of reluctance is called permeance. It is a property or characteristic, which facilitates the creation of flux in a magnetic circuit. This characteristic is identical to the conductance of electrical circuits. It is measured as webers per ampere turns (Wb / AT) or Henry (H). In other words, reciprocal of reluctance is called permeance.

### Reluctivity

It is the reluctance between opposite faces of unit cube (having an equivalent size from all its three sides) of the material. Reluctivity is in fact similar to the resistivity (or specific resistance) of an electric circuit.

### How to find Ampere – Turns

If the average length of a magnetic circuit is and if the circuit consists of N turns, then total ampere turns or m.m.f of the circuit are as follows;

At = NI … (1)

We know that magnetic force (H) of a circuit is equal to the following;

H = NI / or H ℓ = NI … (2)

Entering the value of NI in equation (1), we get;

Ampere turns’ AT = H ℓ … (3)

We know that in case of air, H = B / 𝜇0, otherwise H = B / 𝜇0 𝜇r.  Entering the value of H in equation (3);

∴ AT = H= B ℓ/ 𝜇 = B ℓ / 𝜇0 𝜇r = 0.8 x 106 x B ℓ/ 𝜇r

Or NI = 0.8 x 106 x B ℓ/ 𝜇r

Thus, the following method should be adopted for finding out the total amperes turns of any composite magnetic path;

(i). Find out the value of H of each part of a composite circuit (i.e.., a circuit having more than one magnetic path or routes)

(ii). Find out the ampere – turns of each path by using the following formula;

AT = H x

(iii). Sum up all amperes turns. In this way, total amperes of a complete circuit will be obtained.

### Comparison Between Magnetic and Electric Circuits Similarities

 Magnetic Circuit Electric Circuit Flux = m.m.f / reluctance M.M.F(ampere – turns) Flux Փ (webers) Flux density B (Wb/m2) Reluctance S = I / 𝜇 A [= I/ 𝜇0 𝜇r A] Permeance = I / reluctance Reluctivity Permeability = I / reluctivity Total m.m.f = Փ S1 + Փ S2 + Փ S3 + … Current = e.m.f / resistance E.M.F (volts) Current I (amperes) Current density (A/m2) Resistance R = 𝜌 I/A = I/ 𝜌A Conductance = I / resistance Resistivity Conductivity = I / resistivity Total e.m.f = IR1 + IR2 + IR3+ …