Basic_Electrical_Engineering_4th_edition

CHAPTER

• •
II	Electromagnetic Induction

ii. 1 INTRODUCTION

In 1820 Oersted discovered that a current carrying wire could be made to deflect a freely suspended magnetic needle. Faraday repeated Oersted experiment and went ahead to show that it was not only possible to move the magnet round a current carrying conductor but it was possible for a current carrying wire to move round a magnet. The reason for the phenomenon however remained mystery for quite sometime.

Both Oersted and Ampere's searched this answer from the behavior of the conductor and magnet. However, Faraday concievedthe forces to be due to tension in the medium in which the magnets or conductors were placed. In fact, because of his this approach which led Faraday to introduce the concept of lines of force. In 1831 Faraday showed that electricity could be pro­ duced from magnetism. He demonstrated with the help of simple experiments the current can be made to flow in a circuit whenever (i) current in a neighbouring circuit is made to flow or is interrupted (ii) a magnet is brought near a closed circuit and (iii) a closed circuit is moved near a magnet or a current carrying conductor.

In first case he wound two coils on a toroid, one coil is shorted through a galvanometer and across the other a de source through a switch is connected. When the switch is closed there is sudden change in current during a small time interval and hence there is change in flux link­ ages and voltage is induced in the other circuit whichcirculates current through the galvanom­ eter which gives deflection. He further found that when the battery circuit is switched off, the galvanometer gives deflection again, though in the opposite direction.

In the second and third observation he had a coil shorted through a galvanometer. Here he found that, whenever there is relative motion between the coil and a magnet, the galvanom­ eter gave deflection.

ii.2 FARADAY'S LAWS OF ELECTROMAGNETIC INDUCTION

Faraday's laws state that an emfis induced in a circuit which is

(i)Directly proportional to the time rate of change of flux enclosed by the circuit.

(ii)Directly proportional to N the no. of turns of the circuit.

Combining, the two laws, Faraday's laws ofinduction can be expressed mathematically as

dcp		(ii.l)
e = - N -dt	volts

29

(ii.2)

30	ELECTRICAL ENGINEERING

Here negative signis due to EmilLenz, who subsequentto Faraday's experiments suggested that the direction ofthe induced current is always such as to oppose the action that produced it.

As we know Faraday's law as given by equation (ii.1) is one of the two basic relationships uponwhichthe wholetheoryofelectromagnetic and electromechanical energyconversion devices are based and today we have the generator and motor (electric) operating based on this theory.

Also Faraday was the first to identify emfofselfinduction, i.e., here we have only one coil and it is connected to a de source through a switch. When current is flowing through this coil and the circuit interrupted through the switch an emf is induced in the coil. This is known as

di

emf of self induction expressed mathematically

e=L-dt

Where Lis a proportionalityconstant called the co-efficientofselfinductance which depends uponthe medium and other physical parameter we will discussionin later section ofthis chapter.

ii.3 LENZ'S LAW

As in laws of mechanics, to every action there is an equal and opposite reaction. The fact that this law holds good in electromagnetism was discovered by Emil Lenz.

Lenz law states that this induced current always develops a flux which opposes the very cause it is due to. This law refers to induced currents and therefore, implies that it is applicable to closed circuits only. However, if the circuit is open it is possible to find the direction of in­ duced emf by assuming as if the circuit were closed.

Equation (ii.2) is also known as Lenz's law. In order to study properties of a coil using Lenz's law, thus it is the current changes through the coil rather than flux changes, should be considered. Assume that a voltage Vis required to maintain a constant current I in a coil. The

power			is required to overcome the heating loss in theresistance component ofthe coil. Suppose
	supply voltage Vis increased by an amount +.1V, there is increase in current by +				As per
the		VI	Af	.0.I.
			-. This voltage is in a direction that
equation (ii.2) a voltage e is induced within the coil e = L .0.t

opposes the increase in current. If, however Vis reduced by an amount -.1V, the current I will decrease by an amount - .0.I. The polarity of the induced voltage (- e) is changed and tries to

oppose the reduction in current. The action of opposition within the coil itself is similar to the action encountered in mechanics as a property of a mass called inertia.

ii.4 LAWS OF ELECTROMAGNETIC FORCES

As mentioned earlier Oersted discovered that a current flowing in a conductor deflected the needle of a compass and that the paths of magnetic forces are concentric circle around the conductor. If iron filings are scattered on a cardboard held at right angle to a current carrying conductor the iron filings form in circular patterns.

Ampere experimented with this phenomenon and formulated mathematical expressions describing his observation. Consider two very long parallel conductors separated r metres and carrying currents 11 and 12 as shown in Fig. ii.1 (c).

ELECTROMAGNETIC INDUCTION		-----...	31
,'	.,.-------		- - - - -+-- - - - -
		' ,

(a)(b)

F	--- r - - - -	F

(c)

Fig. ii.1 (a) Two parallel long current carryingl conductor in opposite direction

(b) in same direction (a) a section of the long conductor.

Consider Fig. ii.l(c) where a short length ofthe conductor is shown. Since the currents in the two conductors are flowing in opposite direction; there will beforce ofrepulsion between the two conductors. This is further explainedin Fig. ii.l(a). We find that the fluxlines in the middle add together as the direction of flux lines is the same in the middle space whereas if the two currents were equal there will be no flux line enclosing both the conductors and hence the inner flux lines will pull the two conductor apart 'i.e.' the two will have force of repulsion. However if 11 f:. 12, there will be fewer flux lines enclosing the two conductor and still the pull from the flux between the conductors will be much larger and the conductors will be repelled. However in Fig. ii.l(b) it can be seen from the flux distribution, when the two conductors are carrying current in the same direction, will attract each other. The flux lines within the space cancel out if11 = 12 or else there will be very few and with less intensity and flux lines enclosing both the conductors gets strengthened and hence there will be force of attraction between the two con­ ductors.

From experimentationAmpere'sfoundthattheforce Fis directlyproportional totheproduct of currents in the two conductors and also directly proportional to the length 'l' of the section considered and inversely proportional to distance of separation r between the conductors i.e.

Foe I1rI2l

By using constant of proportionality k equation (ii.3) is rewritten as F= k I1Ir2l

µu

In terms of SI units k is found to be equal to 27t Hence equation (ii.4) becomes

F = 21t 11,1.2 1 Newton

(ii.3)

(ii.4)

(ii.5)

32	0		ELECTRICAL ENGINEERING
Where		is the permeability offree space and its magnitude is
		= 4rc x 10-7 Henry/metre
We alsoµknow that when aµcurrent0			carrying conductor is brought in the domain of a mag­

neticfield, the conductor experiences a force. The direction ofthe force is givenby Fleming's left

hand rule. The length of the current carrying conductor should not be parallel to the magnetic
field. The force will be maximum when the two are perpendicular to each other.
Consider Fig. ii.2. Fig. ii.2 (a) shows two current carrying conductors separated by a
distance r.					l
a		N
	r(a)	I
		t	(b)		(c)
		conductor in a uniform		(c)
	Fig. ii.2 (a) The force between two conductors carrying current, (b) The force on a single
			magnetic field,		The left-hand rule.

The magnetic flux density due to a long conductor a carrying current r is given by

B = µal

2rcr

11 amp at a distance

(ii.6)

and the direction of flux density using cork screw rule will be downward and will be at right angle to the current carrying conductor 'b' with 12 amperes and at a distance r. As mentioned above conductor 'b' is brought in a magnetic flux density B will experience a force which is given by equation (ii.5) and is reproduced and written in a particular fashion.

F = (µol1 ) I2l (ii.7) 2rcr

Now substitutmg. . B £or --µ0I1 from equat10n. ('n..6.)

2rcr

We have F = Blzl Newton (ii.8)

Each of the three quantities F, B and 12 are vector quantities and Fleming's left hand is used to indicate direction of force. Fleming's left-hand rule is stated as follows:

ii.4.1 Fleming's Left Hand Rule

Hold the thumb, the fore finger and the central figure at right angle to each other of the left hand as shown in Fig. ii.2 (c). If the fore-finger points in the direction of magnetic field and the central finger to the direction of current, the thumb will point to the direction of force or motion.