RI Chap 18 Electromagnetic Induction Lecture Notes

18 ELECTROMAGNETIC INDUCTION H2 Physics 9478 Content Page Introduction 2 18.1 Faraday’s Law of Electromagnetic Induction 2 18.2 Magnetic Flux and Magnetic Flux Linkage 3 18.3 Direction of Induced e.m.f. (or Current) 6 18.4 Metal Rod Moving Across a Uniform Magnetic Field 9 18.5 Rotating Disc in a Uniform Magnetic Field 13 18.6 Rotating Coil in a Uniform Magnetic Field (AC Generator) 15 18.7 Practical Applications of Electromagnetic Induction 17 18.8 Transformers 20 Summary 27 Appendix A 28 Appendix B 29 Appendix C 30 Learning Outcomes Candidates should be able to: (a) define magnetic flux as the product of the magnetic flux density and the cross -sectional area perpendicular to the direction of the magnetic flux density. (b) show an understanding of and use the concept of magnetic flux linkage. (c) recall and use φ = BA and N NBAφ = to solve problems, where N is the number of turns. (d) infer from appropriate experiments on electromagnetic induction: (i) that a changing magnetic flux can induce an e.m.f. ; (ii) that the direction of the induced e.m.f. opposes the change producing it ; (iii) the factors affecting the magnitude of the induced e.m.f. (e) recall and solve problems using Faraday's law of electromagnetic induction and Lenz's law. (f) explain simple applications of electromagnetic induction. (g) show an understanding of the principle of operation of a simple iron- core transformer and recall and solve problems using I I= =ss P pps NV NV for an ideal transformer.

Page | 2 Introduction We began our study on the relationship between electricity and magnetism in the previous chapter where we learned that an electric current (or moving charges) produces a magnetic field. As a result, when a current-carrying conductor or a moving charge is w ithin a magnetic field, it will experience a force. In this chapter, we will see that the converse happens. Experiments conducted by Michael Faraday in England in 1831 and independently by Joseph Henry in the United States the same year demonstrated that an e.m.f. could be induced by a changing magnetic field. This effect is known as electromagnetic induction. This discovery greatly revolutionized the production of electricity and has a significant impact on our daily lives. How electromagnetic induction was discovered 18.1 Faraday’s Law of Electromagnetic Induction  Observing Electromagnetic Induction Electromagnetic induction can be demonstrated easily using the laboratory apparatus shown in Fig. 18.1. A bar magnet is moved towards or away from a coil of wire which is connected to a sensitive galvanometer. It is found that: • no current is generated when the magnet is kept stationary relative to the coil (Fig. 18.1(a)), • a current is induced in the coil when the magnet is moved towards (Fig. 18.1( b)) or moved away (Fig. 18.1( c)) from the coi l, and the directions of the currents in the two cases are opposite. • the magnitude of the induced current increases as the magnet moves faster. (a) (b) (c) I = 0 I I I I Magnet moved towards coil Magnet moved away from coil No movement Fig. 18.1 N N N N

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT 3 | Page It is also found that • a current is induced when the coil is moved towards or away from the magnet. • a current is induced when the coil is pulled at 2 ends such that its cross sectional area decreases. The observations in the simple demonstration in Fig. 1 8.1 show that a current is induced as long as there is some change in the magnetic field through the coil. Such an induced current must be produced by an induced e.m.f. This forms the basis of Faraday’s law of electromagnetic induction. The law can be expressed mathematically as: induced e.m.f. = ( )dN dt φ− where Nφ is the magnetic flux linkage of a coil or circuit. To understand the law, we need to know the meaning of magnetic flux and magnetic flux linkage. 18.2 Magnetic Flux and Magnetic Flux Linkage  Magnetic Flux, φ Consider a n area A where a uniform magnetic field of magnetic flux density B passes through at an angle θ to the normal of the area. Faraday's law of electromagnetic induction Faraday’s law of electromagnetic induction states that the induced e.m.f. is proportional to the rate of change of magnetic flux linkage. Magnetic Flux Magnetic flux is defined as the product of the magnetic flux density (through an area) and the cross-sectional area perpendicular to the direction of the magnetic flux density. Formula B θ A Fig. 18.2

Page | 4 Magnetic flux can be thought of as the number of magnetic field lines passing through an area. This clearly depends on (i) B, how strong the magnetic flux density is (stronger fields are represented by closer lines), (ii) A, how big the area is, and (iii) θ, the angle between the area and the magnetic field. The expression for magnetic flux φ is φ = BA cosθ where θ is the angle that the magnetic flux density vector B makes with the normal to the area A. See Fig. 18.3 and Fig. 18.4. Mathematically, this relation can also be expressed in vector notation as BAφ = ⋅  , where A  is the area vector that has a magnitude that is given by the area A and a direction that is normal to the area.  Magnetic Flux Linkage, φN Suppose we have a coil of N turns and uniform cross-sectional area. The expression of magnetic flux linkage is φ=magnetic flux linkage N The S.I. unit for both φ and φN is the weber (Wb). Since φθ= cosN NBA , changing any of the quantities N, B, A and θ will change the magnetic flux linkage of a coil. Making reference to Faraday’s law, e.m.f. can be induced in a coil or circuit when one or more of the following changes are made: • magnitude and direction of B varies with time. • area A of the coil or circuit varies with time. • angle θ between B and the normal to the plane varies with time. Magnetic Flux Linkage The magnetic flux linkage of a coil is defined as the product of the magnetic flux through the coil and the number of turns of the coil. Formula B α A Fig. 18.3 B A Fig. 18.4 If the angle that B makes with the plane of A is given instead, φ = BA sin α If B passes perpendicularly through A, i.e. α = 90º or θ = 0º, φ = BA Formula NOTE!!

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT 5 | Page Example 1 A coil A experiences a change in magnetic flux linkage from 0 to 0.20 Wb at a constant rate in 2.0 s. Another c oil B experiences a change in magnetic flux linkage from 0 Wb to 0.50 Wb at a constant rate in 10.0 s. Calculate the magnitude of induced e.m.f. in each coil. Solution Induced emf in coil A = Induced emf in coil B = It can be seen that although coil B experiences a ___________ change in magnetic flux linkage, it has a ____________ induced e.m.f. The size of the induced e.m.f. is determined by the ________ of change of magnetic flux, not solely on how big the change in magnetic flux is. Example 2 Large alternating currents in a cable can be measured by monitoring the e.m.f. induced in a small coil situated near the cable. This e.m.f. is induced by the varying magnetic field set up around the cable. In which arrangement of coil and cable will the e.m.f. induced be a maximum? Solution The coil in ___ has the largest amount of magnetic flux through it. Hence, it will experience the largest change in magnetic flux linkage when the direction of current in the cable changes. The net magnetic flux through ___ is zero because the magnetic field in one half is pointing ______ of the page , while that in the other half is pointing ______ the page. The magnetic flux t