In this article we will discuss about:- 1. Meaning of Electromagnetism 2. Determination of Direction of Magnetic Field around a Current Carrying Conductor 3. Solenoid 4. Magnetic Circuit 5. Magnetic Circuits with Air-Gaps.
Meaning of Electromagnetism:
A magnet produced by passing an electric current through an insulated wire wound around a core of soft iron, as in the fields of a dynamo or motor, is known as an electromagnet.
Electromagnetism is defined as the phenomena which accompany the production of magnetism by electric currents.
Magnetic Field Due to a Current Carrying Conductor:
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In 1819 it was discovered by a Danish Physicist, Hans Christian Oersted that an electric current is always accomplished by certain magnetic effects.
Oersted found that when current is passed through a conductor placed above the magnetic needle, the needle turns in a certain direction, as shown in Fig. 9.2. He also found that when the direction of flow of current is reversed the magnetic needle also deflects in opposite direction.
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Further investigation showed that the field around the current carrying conductor consists of lines of force, which encircles the conductor. It can be proved experimentally by passing a current carrying conductor AB in the card board and plotting the field with the help of magnetic needle on it, as shown in Figs. 9.3 (a) and 9.3 (b).
From Figs. 9.3 (a) and 9.3 (b) it is observed that when the current is passed through conductor in upward direction, the direction of lines of force is counter-clockwise direction (observed from the top of the conductor) and when the current is passed through the conductor in downward direction, the direction of lines of force is clockwise (observed from the top of the conductor).
The properties of the lines of magnetic induction around a current carrying conductor are summarized as below:
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(i) Lines of magnetic induction are circles, symmetrical about, and concentric with, the axis of the conductor.
(ii) The spacing between the lines of induction decreases as we move closer to the conductor [Fig. 9.3 (c)]
(iii) The direction of lines of magnetic induction depends on the direction of flow of current through the conductor.
(iv) Magnetic induction or flux density depends upon the strength (or magnitude) of the current flowing through the conductor.
Determination of Direction of Magnetic Field around a Current Carrying Conductor:
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The direction of lines of force (magnetic field) around a straight current carrying conductor may be determined by any of the following rules:
1. Cork Screw Rule:
If the right handed cork screw is held with its axis parallel to the conductor pointing the direction of flow of current and the head of the screw is rotated in such a direction that the screw moves in the direction of flow of current then the direction in which the head of screw is rotated, will be the direction of magnetic lines of force.
2. Right Hand Rule:
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If the current carrying conductor is held in right hand by the observer so that it is encircled by fingers stretching the thumb at right angle to the fingers in the direction of flow of current then finger tips will point the direction of magnetic lines of force, as shown in Fig. 9.4 (b).
Solenoid:
The current carrying wire wound spirally in the form of helix about an axis, as shown in Fig. 9.5, is known as solenoid or coil. Magnetic field produced due to current carrying solenoid is fairly uniform over a small region in the middle of the coil. It acts just like a bar magnet having north and south poles.
There are several methods used to determine the polarity of the solenoid.
1. By Use of Compass Needle:
If one of the poles (say north pole) of the compass needle be brought into close proximity to one of the poles of the current carrying solenoid of unknown polarity the action of the compass needle will immediately classify the pole as north or south depending upon whether the needle is repelled or attracted.
2. Helix Rule:
If the helix is held in right hand in such a manner that the finger tips point in the direction of flow of current and thumb is outstretched longitudinally along the coil, it will point towards North Pole (Fig. 9.6).
Magnetic Circuit:
Practically all electric power machinery {e.g. transformers, generators, motors) depend for their operation upon the magnetism produced by the magnetic circuits. The closed path followed by magnetic flux is called a magnetic circuit (Fig. 9.7) just as the closed path followed by current is called an electric circuit.
A magnetic circuit consists of a structure composed for the most part of high permeability magnetic material. The presence of high permeability material causes the magnetic flux to be confined to the paths defined by the structure, much as currents are confined to the conductors of an electric circuit. A simple example of a magnetic circuit is shown in Fig. 9.7. The core is assumed to be composed of magnetic material whose permeability is much greater than that of the surrounding air.
The core is of uniform cross- section and is excited by a winding having N turns and carrying a current of I amperes. This winding develops a magnetic field in the core, as illustrated in the figure. The magnetic field can be visualized in terms of flux lines, which form closed loops interlinking with the winding. According to basic law of magnetic field, called the Ampere’s circuital law (sometimes referred to as Ampere’s work law) the line integral of H around a closed path is equal to the net current enclosed by that path i.e.
The above law is very comprehensive and provides a basis for calculation of magnetic circuits and makes it possible in some cases (such as in the cases of a long current carrying conductor or a long solenoid) to determine readily the strength of the magnetic field.
Magnetic Circuit Concepts:
The flux producing ability of the coil in Fig. 9.7 or of a coil on any other magnetic circuit is proportional to the number of turns N and the current I. The product NI is called the magneto-motive force (mmf) and determines the amount of flux developed in the magnetic circuit.
MMF of the magnetic circuit is the magnetic potential difference that tends to force flux around the magnetic circuit and is analogous to the electromotive force (emf) in an electric circuit.
MMF = NI ampere-turns …(9.2)
The resulting flux ɸ in the magnetic circuit, besides being dependent on the mmf, is also a function of the opposition of the iron to carrying flux. This opposition is called the reluctance S of the magnetic circuit.
As in the case with resistance in the electric circuit, reluctance S of the magnetic circuit is directly proportional to length I, inversely proportional to cross-sectional area a, and dependent on the nature of material of the magnetic circuit.
The reluctance of the magnetic circuit is given as:
S = l/ µ a ampere-turns/weber … (9.3)
When the flux ɸ is constant over the length and uniform over the area. The quantity µ expresses the property of the magnetic material called its permeability. Permeability is a measure of the receptiveness of the material of having magnetic flux developed in it. For free space, the permeability µ0 equals 4 π × 10-7 H/m in the SI system. The relative permeability of magnetic material µr may range up to thousands.
Total flux developed in the circuit is given as:
ɸ = MMF/S webers … (9.4)
The above Eq. (9.4) is sometimes referred to as Ohm’s law for the magnetic circuit. It serves to emphasize the mathematical analogy between the magnetic circuit and the electric circuit. Analogous quantities in the two circuits are listed in Art 9.5.3.
Magnetic circuits differ from electric circuits in one important respect. The reluctance of the magnetic circuit containing iron or ferromagnetic material depends upon the flux carried by it. With the increase in flux, a large change in mmf is required to develop the same change in flux.
Determination of Ampere-Turns:
In any magnetic circuit, flux created is given as:
Hence for determination of AT for a magnetic circuit:
(i) First find field strength H in each part of the magnetic circuit,
(ii) Find the length of various parts of magnetic circuit,
(iii) Find the number of ampere-turns required for the various parts of magnetic circuit from the relation AT = Hl where I is the length of the part in metres and lastly, and
(iv) Find total number of ampere-turns for the whole series magnetic circuit by adding ampere-turns determined for various paths in magnetic circuit.
This will be clearer to the students from examples given in this article.
As both permeability and reluctance may change from one operating condition to another. Hence direct numerical application of the reluctance concept and Eqs. (9.4) and (9.5) is rare. For quantitative analysis, graphical methods are generally used because they can easily be adapted to the non-linearities involved (Art 9.6).
Comparison between Magnetic and Electric Circuits:
Magnetic Circuits with Air-Gaps:
Energy-conversion devices which incorporate a moving element have necessarily air gaps in their magnetic circuits. Air-gaps are also provided in the magnetic circuits to avoid saturation. A magnetic circuit with an air gap is shown in Fig. 9.8. An air-gap is nothing else but a volume of air between two magnetic surfaces. The length of air gap Ig equals the distance between the two magnetic surfaces. The area of x-section of any one of the surfaces gives the air-gap area, ag.
When the air-gap length lg is much smaller than the dimensions of the adjacent core faces, the magnetic flux ɸ is constrained essentially to reside in the core and the air gap and is continuous throughout the magnetic circuit. Thus the configuration shown in Fig. 9.8 can be analysed as a magnetic circuit with two series components, a magnetic or iron core of permeability µ and mean length li and an air-gap of permeability µ0 and length lg.
Since the permeability of air is constant, the air-gap is a linear part of the magnetic circuit and the flux density in the air-gap is proportional to the mmf across the air-gap. The necessary mmf is calculated separately for the air-gap and the iron portions and then added to determine the total mmf.
1. Composite Magnetic Circuits:
Consider a circular ring made from different materials of lengths l1, l2 and l3, cross- sectional areas a1, a2 and a3, and relative permeability µr1, µr2 and µr3 respectively with a cut of length lg known as air-gap. The total reluctance is the arithmetic sum of individual reluctances as they are joined in series.
Or Total ampere-turns required = H1 l1, + H2 l2 + H3 l3 + Hg lg … (9.6)
= Sum of ampere-turns required for individual parts of the magnetic circuit.
2. Parallel Magnetic Circuits:
In series circuits, all parts of the magnetic circuit carry same flux and total ampere-turns required to create a given flux is the arithmetic sum of the ampere-turns required for individual parts of the circuit.
But if the various paths of the magnetic circuit are in parallel, as shown in Fig. 9.10 the ampere-turns required for the combination is equal to the ampere-turns required to create the given flux in one path.
For example for the circuit shown in Fig. 9.10 paths ABCD and AFED are in parallel, so ampere-turns required to create flux ɸ1 in path ABCD is equal to ampere-turns required to create flux ɸ2 in path AFED and also equal to the ampere-turns required for both of the paths.
Hence total ampere-turns required for magnetic circuit shown in Fig. 9.10.
= AT for path DA + AT for path ABCD
= AT for path DA + AT for path AFED
Magnetic Leakage and Fringing:
Leakage flux is the flux, which follows a leaking path, as shown in Fig. 9.11. Flux in the air gap is known as useful flux which is utilized for various useful purposes. For the purpose of calculations the iron is supposed to carry whole of the flux throughout its entire length.
The ratio of total flux (flux in the iron path) to the useful flux (flux in the air) is known as leakage factor.
It is also seen from Fig. 9.11 that the useful flux passing across the gap tends to bulge outwards, thereby increasing the effective area of gap and reducing the flux density in the gap. This effect is referred to as fringing; and the longer the air gap, the greater is the fringing.
In electrical machines (such as in generators and motors), magnetic leakage is undesirable as it causes increase in weight (not decrease in their power efficiency) and cost of manufacture. Though magnetic leakage cannot be avoided completely but can be reduced to the minimum by placing the magnetizing or exciting coils as close as possible to the air gap or to the points in the magnetic circuit where the flux is to be utilized for useful purposes.
The value of leakage factor for modern electric machinery is about 1.2.
Example:
An electromagnet has a gap of 4 mm and flux density in the gap is 1.3 Wb/m2. Determine the ampere-turns for the gap.
Solution:
