ASRJC Electromagnetic Induction Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 17-1 Additional Notes Topic 17: Electromagnetic Induction Content A Magnetic Flux and Magnetic Flux Linkage B Laws of Electromagnetic induction: Faraday’s Law and Lenz’s Law C Induced e.m.f. in a Straight Conductor D Applications of Electromagnetic induction Learning Outcomes Candidates should be able to: (a) define magnetic flux as the product of an area and the component of the magnetic flux density perpendicular to that area. (b) recall and solve problems using  = BA. (c) define magnetic flux linkage. (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. Demonstrating Science Inquiry Skills In 1819, Hans Christian Oersted discovered that a magnetic compass experiences a force in the vicinity of an electric current. This was the first evidence of a relationship between electricity and magnetism. Because nature is often symmetric, it led scientists to suspect that magnetic fields could in turn produce electricity. Indeed, experiments conducted by Michael Faraday showed that a changing magnetic field could induce an electric current in a circuit. The results of the experiment led to what we know today as Faraday’s law, the application of which led to the production of electrical energy in power generation plants throughout the world.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 17-2 Additional Notes Generation of electric current • Faraday first discovered that current can be induced in a circuit by a changing current in a nearby circuit as shown. Fig. 17.1 Action Observation Switch is closed Galvanometer deflects momentarily. Switch remains closed and current is steady Galvanometer shows no deflection. Switch is open Galvanometer deflects momentarily, but in opposite direction. • Faraday went on to observe that when a bar magnet is moved near a coil, a similar effect is obtained. Fig. 17.2 Action Observation Magnet moves towards/ away from coil Galvanometer deflects momentarily. Coil moves towards/ away from magnet Galvanometer deflects momentarily. Faster relative motion between magnet and coil Larger deflection by galvanometer. • Conclusion: (Induced) electric current is generated by a changing magnetic fiel d linking the coil. A galvanometer is an apparatus which deflects to indicate the presence of a current passing through it. It is able to distinguish between 2 currents in opposite directions. Note that there is no e.m.f. source (e.g. battery) in the coil on the left. So any deflection of the galvanometer is surprising. N S Relative motion of the coil and magnet results in a change in the magnetic field linking the coil.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 17-3 Additional Notes A Magnetic flux and Magnetic Flux Linkage • Consider a surface in the presence of a uniform magnetic field, B. Fig. 17.3 • Magnetic flux  through the surface is:  = B┴A = ( Bcos ) A where B┴ = component of B perpendicular to the surface (T) A = area of the surface (m2)  = angle between the B-field and the normal to the area • The SI unit for magnetic flux is weber (Wb). Magnetic flux is the pro duct of an area and the component of the magnetic flux density perpendicular to that area. • For a coil with area A and N number of turns, then the flux linkage through the coil N or total flux passing through the loop is: N = NB┴A = N ( Bcos ) A The Magnetic Flux Linkage in a coil is the product of the area of the coil and the component of the magnetic flux density perpendicular to that area, and the number of turns in the coil. • The SI unit for magnetic flux linkage is Wb (or Wb-turns). It is easier to remember  = B┴A and resolve B to obtain B┴ on your own when solving quantitative questions. Memorizing  = (Bcos) A often poses much confusion as to which angle constitutes the required . Area A refers only to the area that the B-field passes through.  B B┴ Memorise Memorise

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 17-4 Additional Notes Visualising Flux Linkage The amount of magnetic flux linkage can be visualised in terms of the number of B field lines passing through a coil. Check Your Understanding 1 A soft iron ring of variable cross-section has two coils wound around it. One coil has 7 turns. The other, of 3 turns is connected to a d.c. supply. Which quantity is the same inside each coil? A. Magnetic field B. Magnetic flux C. Magnetic flux density D. Magnetic flux linkage Ans: B B Laws of Electromagnetic Induction B.1 Faraday’s Law Faraday determined through experiments that w hen the magnetic flux linking a ci rcuit is changing, an induced e.m.f. is set up in the circuit. Faraday’s Law of Electromagnetic Induction states that the e.m.f. induced in a conductor is proportional to the rate of change of magnetic flux linkage (or rate of cutting of the flux). • For a coil of N turns, the induced e.m.f., ( )dNE dt  dEN dt =− (Units of E: Volt (V)) where the negative sign is a manifestation of Lenz’s Law, which will be discussed in the following section. • The magnitude of E depends on how fast (the rate) the flux linkage changes. Since ( )cos= − = −dN d NBA dt dt E   , E depends on Induced e.m.f. is only formed when there is a change in flux wrt time, not when there is flux. Magnitude of induced e.m.f. depends on the rate of change of flux, not the magnitude of the change. For Fig. 17.4, coil moves from X to Y • Number of field lines linking it increases from 3 to 5 • Or the coil cuts 2 lines in moving from X to Y. Fig. 17.4

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 17-5 Additional Notes ➢ dB dt (rate of change of magnetic flux density perpendicular to area) ➢ dA dt (rate of change of area perpendicular to magnetic field) ➢ ( )cosd dt  (factor dependent on rate of turn of the coil) Worked Example The uniform flux density between the poles of a magnet is 0.080 T. A small coil of area of cross-section 6.5 cm2 has 250 turns and is placed with its plane normal to the magnetic field. The coil is withdrawn from the field in a time of 0.26 s. Determine the average e.m.f. induced in the coil whilst it is being withdrawn. -4 ()() 250(0 0.080)(6.5 10 ) 0.26 0.050 V −  =− =− =−   −=− = fiN B B AN N B Aav t t t Check Your Understanding 2 A uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. The graph shows the variation of the magnitude of the magnetic flux density B with time t. Rank the five regions of the graph according to the magnitude of the e.m.f. induced in the loop, greatest first. Ans: b, d & e tie, a & c tie (zero) ( )cos=− =− d BAdN Ndt dt − dB dt (gradient of vs graph)− B t

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 17-6 Additional Notes Example 1 The figure shows a rectangular conducting loop of resistance R, width l, and length b being pulled at constant speed v through a region of length d in which a uniform magnetic field B is produced by an electromagnet. In this example, l = 40 mm, b = 10 cm, d = 15 cm, R = 1.6 Ω, B = 2.0 T, and v = 1.0 cm s−1. (a) S