Chapter Six ELECTROMAGNETIC INDUCTION

1 INTRODUCTIONE lectricity and magnetism were considered separate and unrelatedphenomena for a long time. In the early decades of the nineteenth century,experiments on electric current by Oersted, Ampere and a few othersestablished the fact that electricity and magnetism are inter-related. Theyfound that moving electric charges produce magnetic fields. For example,an electric current deflects a magnetic compass needle placed in its naturally raises the questions like: Is the converse effect possible?Can moving magnets produce electric currents? Does the nature permitsuch a relation between electricity and magnetism? The answer isresounding yes! The experiments of Michael faraday in England andJoseph Henry in USA, conducted around 1830, demonstratedconclusively that electric currents were induced in closed coils whensubjected to changing magnetic fields.

2 In this Chapter , we will study thephenomena associated with changing magnetic fields and understandthe underlying principles. The phenomenon in which electric current isgenerated by varying magnetic fields is appropriately calledelectromagnetic faraday first made public his discovery that relative motionbetween a bar magnet and a wire loop produced a small current in thelatter, he was asked, What is the use of it? His reply was: What is theuse of a new born baby? The phenomenon of ELECTROMAGNETIC inductionChapter SixELECTROMAGNETICINDUCTIONE lectromagneticInduction205is not merely of theoretical or academic interest but alsoof practical utility. Imagine a world where there is noelectricity no electric lights, no trains, no telephones andno personal computers. The pioneering experiments ofFaraday and Henry have led directly to the developmentof modern day generators and transformers.

3 Today scivilisation owes its progress to a great extent to thediscovery of ELECTROMAGNETIC THE EXPERIMENTS OF faraday ANDHENRYThe discovery and understanding of electromagneticinduction are based on a long series of experiments carriedout by faraday and Henry. We shall now describe someof these shows a coil C1* connected to a galvanometerG. When the North-pole of a bar magnet is pushedtowards the coil, the pointer in the galvanometer deflects,indicating the presence of electric current in the coil. Thedeflection lasts as long as the bar magnet is in galvanometer does not show any deflection when themagnet is held stationary. When the magnet is pulledaway from the coil, the galvanometer shows deflection inthe opposite direction, which indicates reversal of thecurrent s direction.

4 Moreover, when the South-pole ofthe bar magnet is moved towards or away from thecoil, the deflections in the galvanometer are oppositeto that observed with the North-pole for similarmovements. Further, the deflection (and hence current)is found to be larger when the magnet is pushedtowards or pulled away from the coil faster. Instead,when the bar magnet is held fixed and the coil C1 ismoved towards or away from the magnet, the sameeffects are observed. It shows that it is the relativemotion between the magnet and the coil that isresponsible for generation ( INDUCTION ) of electriccurrent in the Fig. the bar magnet is replaced by a second coilC2 connected to a battery. The steady current in thecoil C2 produces a steady magnetic field. As coil C2 is*Wherever the term coil or loop is used, it is assumed that they are made up ofconducting material and are prepared using wires which are coated with When the bar magnet ispushed towards the coil, the pointer inthe galvanometer G Henry [1797 1878] American experimentalphysicist professor atPrinceton University and firstdirector of the SmithsonianInstitution.

5 He made importantimprovements in electro-magnets by winding coils ofinsulated wire around ironpole pieces and invented anelectromagnetic motor and anew, efficient telegraph. Hediscoverd self- INDUCTION andinvestigated how currents inone circuit induce currents HENRY (1797 1878)Physics206moved towards the coil C1, the galvanometer shows adeflection. This indicates that electric current is induced incoil C1. When C2 is moved away, the galvanometer shows adeflection again, but this time in the opposite direction. Thedeflection lasts as long as coil C2 is in motion. When the coilC2 is held fixed and C1 is moved, the same effects are , it is the relative motion between the coils that inducesthe electric above two experiments involved relative motion betweena magnet and a coil and between two coils, another experiment, faraday showed that thisrelative motion is not an absolute requirement.

6 Figure two coils C1 and C2 held stationary. Coil C1 is connectedto galvanometer G while the second coil C2 is connected to abattery through a tapping key Current isinduced in coil C1 due to motionof the current carrying coil Experimental set-up for Experiment is observed that the galvanometer shows a momentary deflectionwhen the tapping key K is pressed. The pointer in the galvanometer returnsto zero immediately. If the key is held pressed continuously, there is nodeflection in the galvanometer. When the key is released, a momentorydeflection is observed again, but in the opposite direction. It is also observedthat the deflection increases dramatically when an iron rod is insertedinto the coils along their MAGNETIC FLUXF araday s great insight lay in discovering a simple mathematical relationto explain the series of experiments he carried out on electromagneticinduction.

7 However, before we state and appreciate his laws, we must getfamiliar with the notion of magnetic flux, B. Magnetic flux is defined inthe same way as electric flux is defined in Chapter 1. Magnetic flux throughInteractive animation on faraday s experiments and Lenz s law: plane of area A placed in a uniform magnetic field B (Fig. ) canbe written as B = B . A = BA cos ( )where is angle between B and A. The notion of the area as a vectorhas been discussed earlier in Chapter 1. Equation ( ) can beextended to curved surfaces and nonuniform the magnetic field has different magnitudes and directions atvarious parts of a surface as shown in Fig. , then the magneticflux through the surface is given by112 2ddB =+ +BABA .. =alldii BA ( )where all stands for summation over all the area elements dAicomprising the surface and Bi is the magnetic field at the area elementdAi.

8 The SI unit of magnetic flux is weber (Wb) or tesla metersquared (T m2). Magnetic flux is a scalar faraday S LAW OF INDUCTIONFrom the experimental observations, faraday arrived at aconclusion that an emf is induced in a coil when magnetic fluxthrough the coil changes with time. Experimental observationsdiscussed in Section can be explained using this motion of a magnet towards or away from coil C1 inExperiment and moving a current-carrying coil C2 towardsor away from coil C1 in Experiment , change the magneticflux associated with coil C1. The change in magnetic flux inducesemf in coil C1. It was this induced emf which caused electriccurrent to flow in coil C1 and through the galvanometer. Aplausible explanation for the observations of Experiment isas follows: When the tapping key K is pressed, the current incoil C2 (and the resulting magnetic field) rises from zero to amaximum value in a short time.

9 Consequently, the magneticflux through the neighbouring coil C1 also increases. It is the change inmagnetic flux through coil C1 that produces an induced emf in coil the key is held pressed, current in coil C2 is constant. Therefore,there is no change in the magnetic flux through coil C1 and the current incoil C1 drops to zero. When the key is released, the current in C2 and theresulting magnetic field decreases from the maximum value to zero in ashort time. This results in a decrease in magnetic flux through coil C1and hence again induces an electric current in coil C1*. The commonpoint in all these observations is that the time rate of change of magneticflux through a circuit induces emf in it. faraday stated experimentalobservations in the form of a law called faraday s law of electromagneticinduction.

10 The law is stated A plane ofsurface area A placed in auniform magnetic field Magnetic field Biat the ith area element. dAirepresents area vector of theith area element.*Note that sensitive electrical instruments in the vicinity of an electromagnetcan be damaged due to the induced emfs (and the resulting currents) when theelectromagnet is turned on or EXAMPLE magnitude of the induced emf in a circuit is equalto the time rate of change of magnetic flux through , the induced emf is given byd dBt =( )The negative sign indicates the direction of and hencethe direction of current in a closed loop. This will bediscussed in detail in the next the case of a closely wound coil of N turns, changeof flux associated with each turn, is the same.