Test 3 General Electrical Engineering

Test 3 General Electrical Engineering

1 common voltage across parallel branches with different voltage sources can be determined by the relation V = (V₁ / R₁ + V₂ / R₂ + V₃ / R₃) / ( 1 / R₁ + 1 / R₂ +1 / R₃ .....) The statement is associated with which theorem ?

A. Superposition theorem. 
B. Thevenin’s theorem. 
C. Norton’s theorem. 
D. Millman’s theorem.Answer

2 The number of independent equations to solve a network is equal to 

A. number of chords. 
B. number of branches. 
C. sum of number of branches and chords. 
D. sum of number of branches , nodes and chords.Answer

3 Which of the following is not a vector ? 

A. Linear momentum. 
B. Angular momentum. 
C. Electric field. 
D. Electric potential.Answer

4 What is the dielectric constant of mica ? 

A. 200. 
B. 100. 
C. 3-8. 
D. 1-2.Answer

5 Magnetic moment is a 

A. pole strength. 
B. universal constant. 
C. scalar quantity. 
D. vector quantity.Answer

6 Temporary magnets are used in which of the following ? 

A. Loud speakers. 
B. Generators. 
C. Motors. 
D. All of these.Answer

7 Autotransformer makes effective saving on copper and copper losses, when its transformation ratio is equal to 

A. approx to one. 
B. less than one. 
C. greater than one. 
D. none of the above.Answer

8 The noise resulting from vibrations of laminations set by magnetic forces, is termed as 

A. magnetostriction. 
B. boo. 
C. hum. 
D. zoom.Answer

9 In circle diagram for induction motor, diameter of circle represents which of the following ? 

A. Slip. 
B. Rotor current. 
C. Running torque. 
D. Line voltage.Answer

10 Tarapur nuclear power plant has which type of reactor? 

A. Pressurized water reactors. 
B. Boiling water type. 
C. CANDU type reactors. 
D. None of these.Answer

Test 2 General Electrical Engineering

1 25 kV, 50 Hz, 1 - φ supply is used for supplying power to the locomotives throughout India except which zone ? 

A. West. 
B. East. 
C. South. 
D. North-East.Answer

2 Three resistors, each of R ohms, are connected to form a triangle. The resistance between any two terminals will be 

A. 3 / 2 R. 
B. 2 / 3 R. 
C. R / 2. 
D. 3R.Answer

3 A 100 W bulb is connected in series with a room heater. If now 100 W bulb is replaced by a 40 w bulb, the heater output will 

A. decrease 
B. increase 
C. remain the same 
D. unjustifiedAnswer

4 Which of the following statements is false in case of a series circuit? 

A. The current flowing through each resistor is the same. 
B. The voltage drop across each resister is same. 
C. Resistors are additive. 
D. All of above are false.Answer

5 Which of the following quantities are same in all parts of a series circuit? 

A. Current. 
B. Resistance. 
C. Voltage. 
D. Power.Answer

6 Conductance is the reciprocal of what? 

A. Resistance. 
B. Inductance. 
C. Reluctance. 
D. Capacitance.Answer

7 You have to replace 1500 Ω resistor in radio. You do not have any 1500 Ω resistor but have several 1000 Ω ones which way you would connect them ? 

A. Two in parallel. 
B. Two in parallel and one in series. 
C. Three in parallel. 
D. Three in series.Answer

8 Bulbs in street lightning are all connected in which format? 

A. Parallel. 
B. Series. 
C. Series-parallel. 
D. End to end.Answer

9 1 newton metre (N - m) = ? 

A. One watt. 
B. One joule. 
C. One joule second. 
D. Five joules.Answer

10 In a delta network each element has value R. The value of each element in equivalent star network will be equal to 

A. R / 6. 
B. R /4. 
C. R / 2. 
D. R / 3.Answer

Test 1 General Electrical Engineering

1 Insulated cables are usually rated by their : 

A. operating voltage. 
B. operating voltage and highest operating temperature 
C. operating temperature 
D. costAnswer

2 What is cable tray? 

A. Cable tray is a cover for many insulatated cables. 
B. Cable tray is a protective layer. 
C. Cable tray is a rating of cables. 
D. Cable tray is a metalic sheild used to protect cables.Answer

3_________ cannot sustain much voltage fluctuations. 

A. Sodium vapour lamp. 
B. Mercury vapour lamp. 
C. Incandescent lamp. 
D. Fluorescent lamp.Answer

4 Class B insulators can bear temperature (in degree centigrade) upto

A. 130. 
B. 120. 
C. 105. 
D. 90.Answer

5 Excess 3 code is known as?

A. Weighted code 
B. Cyclic redundancy code. 
C. Self complementing. 
D. Algebraic code.Answer

6 Permittivity of free space is equal to

A. 8.854 × 10-09. 
B. 8.854 × 10-12. 
C. 9 × 10 09. 
D. 1.Answer

7 Capacitor banks are connected with ac induction motor

A. in parallel. 
B. in series. 
C. not connected at all. 
D. can be connected either way –series / parallel.Answer

8 By looking at which part of the motor it can be easily confirmed that a particular motor is D.C motor? 

A. Frame. 
B. Shaft. 
C. Commutator. 
D. Stator.Answer

9 In regenerative braking which of the following is true? 

A. Motor energy is dissipated as heat. 
B. Motor energy is dissipated in armature heating. 
C. Motor energy is dissipated in windage losses. 
D. Motor is made to run as generator.Answer

10 Which of the following statements regarding single-phase induction motor is correct? 

A. It requires only one winding. 
B. It can rotate in one direction only. 
C. It is self starting. 
D. It is not self starting.Answer

Vacuum Switchgear

Vacuum Switchgear

Now days, vacuum switchgear getting popularity very rapidly. In medium voltage switchgear application, medium voltage vacuum switchgear ranges from 3 to 36 KV. Now days, vacuum interruption technology, in medium voltage application, dominates, air, SF₆ and oil technologies. Since, vacuum circuit breaker is more safely and reliably operated where number of faulty and normal operation is much high.

Vacuum as an Interruption Medium

The performance of a circuit breaker mainly depends upon the dielectric medium used for arc quenching. Another major advantage of this technology, is that vacuum switchgear is nearly maintenance free.

Now we will discuss one the different features of this technology, which make it so popular-

Dielectric Strength of Vacuum

For a given contact gap, vacuum provides, about eight times more dielectric strength than air and four times more dielectric strength than SF₆ gas at one bar. As the dielectric strength is so high, the contact gap of vacuum circuit breaker can be maintained very small. In this small contact gap, arc quenching is safely possible due to high dielectric strength and also vacuum has the fast recovery strength after full arc interruption to its full dielectric value at electric current zero. This makes, vacuum switchgear, most suitable for capacitor switching.

Law Arc Energy in Vacuum

The energy dissipated during arc in vacuum is about one tenth of that of oil and one fourth of that of SF₆ gas. Law energy dissipation mainly due to low interruption time (due to small contact gap) and small arc length (this is also due to small contact gap). Because of this low arc energy dissipation, vacuum switchgear has negligible contact erosion and this gives it nearly maintenance free life span. It is also to be noted that, for breaking certain current, the energy required by vacuum circuit breaker is minimum compared to air circuit breaker and oil circuit breaker.

Simple Driving Mechanism

In SF₆, oil and air circuit breaker, movement of contacts is highly resisted by highly compressed medium of arc quenching chamber. But in vacuum switchgear, there is no medium, and also movement of contacts is quit less due to its small contacts gap, hence driving energy required is much smaller, in this circuit breaker. That is why simple spring-spring operating mechanism is sufficient for this switchgear system, no need of hydraulic and pneumatic mechanism. Simpler driving mechanism gives a high mechanical life of vacuum switchgear.

Rapid Arc Quenching

During opening of contacts in electric current carrying condition, metal vapor is produced between the contacts, and this metal vapor provides a path through which electric current continuous to flow until the next electric current zero. This phenomenon is also known a vacuum arc. This arc is extinguished near the electric current zero and the conductive metal vapor is re-condensed on the contact surface in a matter of micro seconds. It has been observed that, only 1% of the vapor is re-condensed on arc chamber’s side wall, and 99% of vapor re-condensed on the contact surface from where it was vaporized.

From above discussion, it is almost clear that, the dielectric strength of vacuum switchgear recovers very fast and contact erosion is almost negligible.

It has been observed that, up to 10 KA, the arc remains diffused. It takes the form of vapor discharge and covers the entire contact surface. But above 10 KA, the diffused arc is concentrated at central point of the contact surface due to its own magnetic field. Due to this phenomenon, the center of the contacts over heated. This problem can be solved by providing specially designed contact surface so that, the arc can travel throughout the surface area, instead of being stationery at certain point. Different manufacturers use different contact surface designs to chive this travelling of arc due to its own magnetic field. This causes minimum and uniform contact erosion.

Vacuum Arc

Vacuum Arc

As there is no such media the arc in vacuum circuit breaker differs from general arc in circuit breaker. In vacuum arc the electrons, ions and atoms are all derived from the electrodes itself. The absolute vacuum is not practically possible to create so there are some gases in practical vacuum chamber but the gas pressure here is so low that it does not have any significant role in conduction process during arc. In this sense the vacuum arc is therefore really a metal vapour discharge. The vacuum arc can be divided into two main regions, the cathode region and the plasma region.

Cathode Region of Arc Plasma

The vapour necessary to sustain vacuum arc comes mainly from the cathode spots. Each spot carries a mean electric current dependent on the cathode material, which is about 100 A for copper. The electric current density at the spots is estimated to be 10¹⁰ - 10¹¹ A/m², depending on the cathode material. The cathode spots move on the cathode surface. At higher electric current the numbers of cathodes spots is increased due to repulsion the motion of parallel spots and their movements become more random.

Whenever the electric current carrying contacts open in a circuit breaker, cathode spots are formed depending upon the electric current flowing through the contacts. At high electric current multiple numbers of cathode spots formed which constitute the main source of vapour for the arc in vacuum circuit breaker. The cathode surface in normally not perfectly smooth and may have many micro projections on the surface. When electric current carrying contacts are being separated in a vacuum circuit breaker the electric current flowing in the circuit will be concentrated at those projections as they form the last point of contacts. Due to their small area of contact the projections are sufficiently heated up and they suffer explosive evaporation and supply the vapour for formation of arc in vacuum circuit breaker.

The vapour which has high density at the cathode spot, expands into the vacuum and perhaps at a distance of 10 mm from the cathode. The an electron traversing the inter electrode gap experiences condition of high pressure near the cathode where the mean free path is quite less than that of low pressure in the plasma where it is the order of 10 mm.

At low currents, the voltage drop in the plasma region of low electric current is negligible. The voltage gradient is less than 0.01 V/mm. At high current, the gradient may be increased up to a few V/mm.

Stability of Vacuum Arc

The power frequency electric current passes through the contacts in circuit breaker, crosses electric current zero point 100 times in a second. It is always desirable to interrupt the electric current during it passes the zero value otherwise there will be electric current chopping effect which may causes switching over voltage in the system. Therefore, it is necessary to interrupt the arc as long as it is stable for a half cycle duration particularly it should continue to exist when the electric current approaches to zero. The stability of arc in vacuum circuit breaker depends upon the contact materials, pressure of metal vapor and circuit parameters such as voltage, current, inductor and capacitance. It is observe that higher vapour pressure in low temperature is better stability of arc. Some metals like Zn, Bi also show better stability of vacuum arc. Like vapour pressure thermal conductivity of contact material is also a major factor regarding stability of vacuum arc in circuit breaker. If the contact metal is good conductor of heat, the contact surface temperature will fall in faster rate thus metal vapour will be condensed fast hence due to the lack of vapor the vacuum arc will be interrupted. But if the metal used for circuit breaker contacts is bad conductor of heat, the metal vapour will not condense fast and the arc continues thus vacuum arc in circuit breaker becomes stable. For successful and safe electric current interruption in vacuum circuit breaker, both arc extinction at proper point of time and the stable arc are required. It is observed that the metal having high boiling and melting point gives low vapour in high temperature but in the same time it becomes poor conductor. Again the metal having low melting and boiling points gives more vapour at high temperature and in the same time it becomes good conductor. Therefore, to combine these contradictory properties in one single material, alloys of two or more metals or a metal and nonmetal have to be made. Some example of alloys used as the materials to make vacuum circuit breaker contacts are copper–bismuth, silver–lead, copper–lead etc.

Extinction of Vacuum Arc

Successful electric current interruption by a vacuum arc depends upon how fast the metal vapour is condensed into the anode and shield near at electric current zero. At electric current zero crossing the numbers of cathode spots are decreased to very few as the electric current falls and ultimately becomes zero at exact electric current zero. The metal vapour density becomes also very less because during this electric current zero maximum metal vapour is condensed into anode and shield. The density of metal vapour becomes so low throughout the gap during zero crossing that the gap is substantially becomes an insulator which prevents re-ionization of vacuum arc in circuit breaker after electric current zero.

Arc in Circuit Breaker

Arc in Circuit Breaker

What is Arc ?

During opening of electric current carrying contacts in a circuit breaker the medium in between opening contacts become highly ionized through which the interrupting electric current gets low resistive path and continues to flow through this path even the contacts are physically separated. During the flowing of electric current from one contact to other the path becomes so heated that it glows. This is called arc.

Arc in Circuit Breaker

Whenever, on load current contacts of circuit breaker open there is an arc in circuit breaker, established between the separating contacts. As long as this arc is sustained in between the contacts the electric current through the circuit breaker will not be interrupted finally as because arc is itself a conductive path of electricity. For total interruption of electric current the circuit breaker it is essential to quench the arc as quick as possible. The main designing criteria of a circuit breaker is to provide appropriate technology of arc quenching in circuit breaker to fulfill quick and safe electric current interruption. So before going through different arc quenching techniques employed in circuit breaker, we should try to understand "e;what is arc"e; and basic theory of arc in circuit breaker, let’s discuss.

Thermal Ionization of Gas

There are numbers of free electrons and ions present in a gas at room temperature due to ultraviolet rays, cosmic rays and radioactivity of the earth. These free electrons and ions are so few in number that they are insufficient to sustain conduction of electricity. The gas molecules move randomly at room temperature. It is found an air molecule at a temperature of 300°K (Room temperature) moves randomly with an approximate average velocity of 500 meters/second and collides other molecules at a rate of 10¹⁰times/second. These randomly moving molecules collide each other in very frequent manner but the kinetic energy of the molecules is not sufficient to extract an electron from atoms of the molecules. If the temperature is increased the air will be heated up and consequently the velocity on the molecules increased. Higher velocity means higher impact during inter molecular collision. During this situation some of the molecules are disassociated in to atoms. If temperature of the air is further increased many atoms are deprived of valence electrons and make the gas ionized. Then this ionized gas can conduct electricity because of sufficient free electrons. This condition of any gas or air is called plasma. This phenomenon is called thermal ionization of gas.

Ionization due to Electron Collision

As we discussed that there are always some free electrons and ions presents in the air or gas but they are insufficient to conduct electricity. Whenever these free electrons come across a strong electric field, these are directed towards higher potential points in the field and acquire sufficiently high velocity. In other words, the electrons are accelerated along the direction of the electric field due to high potential gradient. During their travel these electrons collide with other atoms and molecules of the air or gas and extract valance electrons from their orbits. After extracted from parent atoms, the electrons will also run along the direction of the same electric field due to potential gradient. These electrons will similarly collide with other atoms and create more free electrons which will also be directed along the electric field. Due to this conjugative action the numbers of free electrons in the gas will become so high that the gas stars conducting electricity. This phenomenon is known as ionization of gas due to electron collision.

Deionization of Gas

If all the cause of ionization of gasare removed from an ionized gas it rapidly come back to its neutral state by recombination of the positive and negative charges. The process of recombination of positive and negative charges is known as deionization process. In deionization by diffusion, the negative ions or electrons and positive ions move to the walls under the influence of concentration gradients and thus completing the process of recombination.

Role of Arc in Circuit Breaker

When two electric current contacts just open, an arc bridges the contact gap through which the electric current gets a low resistive path to flow so there will not be any sudden interruption of current. As there is no sudden and abrupt change in electric current during opening of the contacts, there will not be any abnormal switching over voltage in the system. If i is the electric current flows through the contacts just before they open, L is the system inductance, switching over voltage during opening of contacts, may be expressed as V = L.(di/dt) where di/dt rate of change of electric current with respect to time during opening of the contacts. In the case of alternating electric current arc is monetarily extinguished at every electric current zero. After crossing every electric current zero the media between separated contacts gets ionized again during next cycle of electric current and the arc in circuit breaker is reestablished. To make the interruption complete and successful, this re-ionization in between separated contacts to be prevented after a electric current zero.

If arc in circuit breaker is absence during opening of electric current carrying contacts, there would be sudden and abrupt interruption of electric current which will cause a huge switching over voltage sufficient to severely stress the insulation of the system. On the other hand, the arc provides a gradual but quick, transition from the electric current carrying to the electric current breaking states of the contacts.

Arc Interruption or Arc Quenching or Arc Extinction Theory

Arc Column Characteristics

At high temperature the charged particles in a gas are rapidly and randomly move, but in absence of electric field, no net motion is occurred. Whenever an electric field is applied in the gas, the charged particles gain drift velocity superimposed on their random thermal motion. The drift velocity is proportional to the voltage gradient of the field and particle mobility. The particle mobility depends upon the mass of the particle, heavier particles, lower the mobility. The mobility also depends upon mean free paths available in the gas for random movement of the particles. Since every time a particle collides, it losses its directed velocity and has to be re-accelerated in the direction of electric field again. Hence net mobility of the particles is reduced. If the gas is in highly pressure, it becomes denser and hence, the gas molecules come closer to each other, therefore collision occurs more frequently which lowers the mobility particles. The total electric current by charged particles is directly proportional to their mobility. Therefore the mobility of charged particles depends upon the temperature, pressure of the gas and as well as nature of the gas. Again the mobility of gas particles determines the degree ionization of gas.

So from above explanation we can say that ionization process of gas depends upon nature of gas (heavier or lighter gas particles), pressure of gas and temperature of gas. As we said earlier the intensity of arc column depend up on the presence of ionized media between separated electrical contacts, hence, special attention should be given in reducing ionization or increasing deionization of media between contacts. That is why the main designing feature of circuit breaker is to provide different pressure control methods, cooling methods for different arc media in between circuit breaker contacts.

Heat loss from Arc

Heat loss from arc in circuit breaker is taken place through conduction, convection as well as radiation. In circuit breaker with plain break arc in oil, arc in chutes or narrow slots nearly all the heat loss due to conduction. In air blast circuit breaker or in breaker where a gas flow is present between the electrical contacts, the heat loss of arc plasma occurs due to convection process. At normal pressure the radiation is not a significant factor but at higher pressure the radiation may become a very important factor of heat dissipation from arc plasma. During opening of electrical contacts, the arc in circuit breaker is produced and it is extinguished at every zero crossing of the electric current and then it is again reestablished during next cycle. The final arc extinction or arc quenching in circuit breaker is achieved by rapid increase of the dielectric strength in the medium between the contacts so that reestablishment of arc after zero crossing cannot be possible. This rapid increase of dielectric strength in between circuit breaker contacts is achieved either by deionization of gas in the arc media or by replacing ionized gas by cool and fresh gas.

There are various deionization processes applied for arc extinction in circuit breaker, let us discussed in brief.

Deionization of Gas due to Increasing Pressure

If pressure of the arc path increases, the density of the ionized gas is increased which means, the particles in the gas come closer to each other and as a result the mean free path of the particles is reduced. This increases the collision rate and as we discussed earlier at every collision the charged particles loss their directed velocity along electric field and again they are re-accelerated towards field. It can be said that over all mobility of the charged particles is reduced so the voltage required to maintain the arc is increased. Another effect of the increased density of particles is a higher rate of deionization of gas due to the recombination of oppositely charged particles.

Deionization of Gas due to Decreasing Temperature

The rate of ionization of gas depends upon the intensity of impact during collision of gas particles. The intensity of impact during collision of particles again depends upon velocity of random motions of the particles. This random motion of a particle and its velocity increases with increase of temperature of the gas. Hence it can be concluded like that if temperature of a gas is increased; its ionization process is increased and opposite statement is also true that is if the temperature is decreased the rate of ionization of gas is decreased means deionization of gas is increased. Therefore more voltage required to maintain arc plasma with a decreased temperature. Finally it can be said that the cooling effectively increases the resistance of the arc.

Different types of circuit breakers employ different cooling techniques which we will discuss later in the course of circuit breakers.

Electrical Circuit Breaker

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Electrical Circuit Breaker

What is Circuit Breaker?

Definition of circuit breaker : - Electrical circuit breaker is a switching device which can be operated manually as well as automatically for controlling and protection of electrical power system respectively. As the modern power system deals with huge currents, the spacial attention should be given during designing of circuit breaker to safe interruption of arc produced during the operation of circuit breaker. This was the basic definition of circuit breaker.

Introduction to Circuit Breaker

The modern power system deals with huge power network and huge numbers of associated electrical equipment. During short circuit fault or any other types of electrical fault these equipment as well as the power network suffer a high stress of fault electric current in them which may damage the equipment and networks permanently. For saving these equipment and the power networks the fault electric current should be cleared from the system as quickly as possible. Again after the fault is cleared, the system must come to its normal working condition as soon as possible for supplying reliable quality power to the receiving ends. In addition to that for proper controlling of power system, different switching operations are required to be performed. So for timely disconnecting and reconnecting different parts of power system network for protection and control, there must be some special type of switching devices which can be operated safely under huge electric current carrying condition. During interruption of huge current, there would be large arcing in between switching contacts, so care should be taken to quench these arcs in circuit breaker in safe manner. The circuit breaker is the special device which does all the required switching operations during electric current carrying condition. This was the basic introduction to circuit breaker.

Working Principle of Circuit Breaker

The circuit breaker mainly consists of fixed contacts and moving contacts. In normal "on" condition of circuit breaker, these two contacts are physically connected to each other due to applied mechanical pressure on the moving contacts. There is an arrangement stored potential energy in the operating mechanism of circuit breaker which is realized if switching signal given to the breaker. The potential energy can be stored in the circuit breaker by different ways like by deforming metal spring, by compressed air, or by hydrolic pressure. But whatever the source of potential energy, it must be released during operation. Release of potential energy makes sliding of the moving contact at extremely fast manner. All circuit breaker have operating coils (tripping coils and close coil), whenever these coils are energized by switching pulse, the plunger inside them displaced. This operating coil plunger is typically attached to the operating mechanism of circuit breaker, as a result the mechanically stored potential energy in the breaker mechanism is released in forms of kinetic energy, which makes the moving contact to move as these moving contacts mechanically attached through a gear lever arrangement with the operating mechanism. After a cycle of operation of circuit breaker the total stored energy is released and hence the potential energy again stored in the operating mechanism of circuit breaker by means of spring charging motor or air compressor or by any other means. Till now we have discussed about mechanical working principle of circuit breaker. But there are electrical characteristics of a circuit breaker which also should be consider in this discussion of operation of circuit breaker.

Let's have a discussion on electrical principle of circuit breaker.

The circuit breaker has to carry large rated or fault power. Due to this large power there is always dangerously high arcing between moving contacts and fixed contact during operation of circuit breaker. Again as we discussed earlier the arc in circuit breaker can be quenching safely if the dielectric strength between the electric current carrying contacts of circuit breaker increases rapidly during every electric current zero crossing of the alternating current. The dielectric strength of the media in between contacts can be increased in numbers of ways, like by compressing the ionized arcing media since compressing accelerates the deionization process of the media, by cooling the arcing media since cooling increase the resistance of arcing path or by replacing the ionized arcing media by fresh gasses. Hence a numbers of arc quenching processes should be involved in operation of circuit breaker.

Types of Circuit Breaker

According different criteria there are different types of circuit breaker.
According to their arc quenching media the circuit breaker can be divided as-

Oil circuit breaker.

Air circuit breaker.

SF₆ circuit breaker.

Vacuum circuit breaker.

According to their services the circuit breaker can be divided as-

Outdoor circuit breaker

Indoor breaker.

According to the operating mechanism of circuit breaker they can be divided as-

Spring operated circuit breaker.

Pneumatic circuit breaker.

Hydrolic circuit breaker.

According to the voltage level of installation types of circuit breakerare referred as-

High voltage circuit breaker.

Medium voltage circuit breaker.

Low voltage circuit breaker.

Magnetic Material

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Magnetic Material

All the materials in this universe may be classified either magnetic or non-magnetic. Magnetic materials are those which are affected by magnetic field and non magnetic materials are those which are not affected or slightly affected by magnetic field. Maximum types of materials fall under category of non – magnetic material. Non-magnetic material can further be classified as diamagnetic and paramagnetic materials. Some of the non magnetic materials exhibit very slight magnetic effect but it is extremely difficult to detect. Practically, all these materials are referred as totally non-magnetic. On the other hand, all the materials which exhibit magnetic effect strongly are referred as magnetic materials or ferromagnetic materials. The materials based on iron, cobalt and ferrites are normally ferromagnetic materials. 

Magnetic Field

Magnetic fields can be created either by placing, a permanent magnet or by supplying electric current through a solenoid. Latter is electromagnet. A magnetic field is defined as the space surrounding a permanent magnet or electromagnet where the electric field is felt by other magnet or magnetic material.

Magnetic Flux or Magnetic Lines of Force

Magnetic field is also represented by lines of force as static electric field. These lines of force are referred as magnetic flux. When a unit magnetic pole is placed inside a magnetic field, it will experience both repulsive and attractive force, from similar and opposite poles of the magnet, respectively. The unit pole travels due to resultant of the repulsive and attractive force. The path through which the unit pole travels in the magnetic field is referred as magnetic lines of force. There are numbers of magnetic lines of force in a magnetic field, and these lines of force are collectively called magnetic flux. These flux lines have some specific properties that are described below.

Magnetic Flux Density Due to a Current Carrying Conductor

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Magnetic Flux Density Due to a Current Carrying Conductor

Whenever a electric current passes through a conductor, a magnetic field is appeared surrounding it. The direction of this magnetic field of electric current carrying conductor can be determined by Cork Screw rule or Right Hand rule.

As per Biot Savart’s law, the expression of magnetic flux density at a point P nearer to a conductor carrying a electric current ‘I’ is given as,

Where, dB is the infinitesimal flux density at point P. 

Current I is passing through the conductor.

dl is infinitesimal length of conductor.

r is the radius vector from center of element dl to point P.

θ is the angle between electric current and radius vector.

Flux Density due to Current Carrying Conductor

Now in order to find the actual magnetic flux density B at the point P due to total length of the conductor, we have to integrate the expression of dB, in respect of dl.

The above expression is used to evaluate magnetic flux density B at any point due to infinitely long linear conductor and this comes as

Here, R is the radial distance from conductor to the point P.

Now if we integrate B around a path of radius R enclosing the electric current carrying conductor, we get

This equation shows that the integral of H around a closed path is equal to the current enclosed by the path. This is nothing but Ampere’s law. If the path of integration enclosed N number of turns of wire, each with a electric current I in the same direction, then

This relation is very important relation; it is used for determining flux linkage of a system of conductors. From flux linkage, the inductor of the system can easily be determined.

If the electric current in the conductor varies, it causes variation of flux linkage. We know that change of flux linkage induces a voltage in the conductors and the rate of change of flux linkage is directly proportional to the induced voltage. This is known as Faraday’s laws of electromagnetic induction.

Magnetic Effects of Electric Current

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Magnetic Effects of Electric Current

Magnetic Field due to Current Carrying Conductor

In 1819, it was discovered by a Danish Physicist, Hans Christian Oersted that an electric current is always accomplished by certain magnetic effect. He observed a electric current carrying conductor when placed near a magnetic needle; the needle deflects to a certain direction. He also observed that when the direction of electric current in the conductor is reversed, the needle deflects in opposite direction. 

That means there is a magnetic field due to electric current carrying conductor. Further investigation shows that, the magnetic field around the conductor consists of a number of concentric closed lines of force. If we pass an electric current through a conductor through a card board as shown in the figure and try to plot the field with the help of a magnetic needle on that card board, we shall get the magnetic lines as shown in figure. These are all closed circles and concentric with the conductor. Now if we reverse the electric current in the conductor and repeat the same experiment as shown in the figure, we shall get the oppositely directed closed circular magnetic lines, concentric with the conductor as shown. 

From the above experiment it is also found that when electric current flows through the conductor in upward direction, the direction of circular magnetic lines are anti clockwise if we observe from the top. On the other hand; if the electric current flows through the conductor in downward direction, the circular magnetic lines are clockwise if we observe from the top.

Properties of magnetic field due to a electric current carrying conductor can be summarized as below,

1. All lines of magnetic field are circular in shape, symmetrical to each other and concentric with the axis of electric current carrying conductor.

2. The radius of the lines of force increases as we go away from the axis of the conductor.

3. The direction of magnetic circular line depends upon the direction of flow of electric current through the conductor.

4. The magnetic flux density of the induced magnetic field around the conductor increases if the electric current flowing through the conductor is increased and it decreases if the electric current is decreased.

Determination of Direction of magnetic field around a Current Carrying Conductor.

There are mainly two popular rules for determining the direction of magnetic field due to a electric current carrying conductor and these are Cork screw rule and Right hand rule.

If the right handed cork screw is held with its axis parallel to the conductor pointing the direction of flow of electric current and the head of the screw is rotated in such a direction that the screw moves in the direction of flow of electric current , then the direction in which the head of screw is rotated, will be the direction of magnetic lines of force.

Right Hand Rule 

If the electric current carrying conductor is held in right hand by the observer so that it is encircled by fingers stretching the thumb at right to the fingers in the direction of flow of electric current then finger tips will point the direction of magnetic lines of force.