1© Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field E.m.f. induced in coil Magnetic flux (  ) Laws of Electromagnetic Induction Factors affecting the magnitude of induced e.m.f.

2 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 252) E.m.f. induced in coil 1. Relative motion between conductor and magnetic field - N-pole of a bar magnet is pushed into a coil of wire - the coil experiences a change of B-field - e.m.f. is induced and current flows This effect of producing an e.m.f. using magnetism is known as electromagnetic induction. Go to More to Know 1 More to Know 1

3 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 253) E.m.f. induced in coil 2. Stationary conductor in a changing magnetic field - current flows in A - induced e.m.f. produced in B - current flows

4 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 253) Magnetic flux (  ) magnetic flux (  ) - product of magnetic flux density (B) and area of right angles to B-field (A)  = BA  = BA cos  Unit: weber (Wb) 1 Wb = 1 T m 2 Go to More to Know 2 More to Know 2 Go to More to Know 3 More to Know 3

5 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 254) Laws of Electromagnetic Induction When the magnetic flux linkage through a circuit changes, an e.m.f. which is directly proportional to the rate of change of magnetic flux linkage is induced. (a) Faraday’s Law of Electromagnetic Induction

6 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 254) Laws of Electromagnetic Induction The direction of the induced current is such as to oppose the change which gives rise to it. (b) Lenz’s Law

7 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 255) Laws of Electromagnetic Induction 1. Induced e.m.f. in an one-turn coil (a) Case 1: Relative motion between conductor and magnetic field - push or move a bar magnet out of a coil -  enclosed by coil increases or decreases - induced e.m.f. is produced

8 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 256) Laws of Electromagnetic Induction (b) Case 2: Stationary conductor in a changing magnetic field - current in A increases or decreases -  enclosed by B increases or decreases - induced e.m.f. is produced

9 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 256) Laws of Electromagnetic Induction 2. Induced e.m.f. in a coil having N turns Total flux linkage = No. of turns x Magnetic flux enclosed by on-turn coil = N  or NBA

10 © Manhattan Press (H.K.) Ltd E.m.f. induced in a coil in a changing magnetic field (SB p. 257) Factors affecting the magnitude of induced e.m.f. Increase magnitude of induced e.m.f. by 1. Increasing relative motion between magnet and coil (larger the rate of change of  ) 2. Using stronger magnet (larger the rate of change of  ) 3. Increasing no. of turns of coil (larger N) Go to Example 1 Example 1 Go to Example 2 Example 2

11 © Manhattan Press (H.K.) Ltd. End

12 © Manhattan Press (H.K.) Ltd. Induced current in closed circuit An e.m.f. is induced in both an open and closed circuits. A current is induced only in a closed circuit. Return to Text 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 253)

13 © Manhattan Press (H.K.) Ltd. Magnetic flux density and magnetic flux The magnetic flux density (B) is equal to the magnetic flux (Φ) per unit area. Return to Text 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 254)

14 © Manhattan Press (H.K.) Ltd. The area A is a vector whose direction is normal to the surface. Return to Text 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 254)

15 © Manhattan Press (H.K.) Ltd. Q: Q: (a) Calculate the values of the magnetic flux density B and the magnetic flux Φ within an air-cored solenoid of diameter 2.50 cm and turns per metre when a current of 0.10 A flows. (b) How do these values change when the solenoid is filled with a material of relative permeability 5 000? 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 257) Solution

16 © Manhattan Press (H.K.) Ltd. Solution: (a) Magnetic flux density within the solenoid (B) = μ 0 nI = (4π ×10 –7 ) ×2 000 ×0.10 = 2.51 ×10 –4 T Magnetic flux within the solenoid (Φ) = BA = Bπr 2 (b) When the solenoid is filled with a material of μ r = 5 000, Magnetic flux density (B’) = μ r B = ×(2.51 ×10 –4 ) = 1.26 T Magnetic flux (Φ’) = μ r Φ = ×(1.23 ×10 –7 ) = 6.17 ×10 –4 Wb Return to Text 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 257)

17 © Manhattan Press (H.K.) Ltd. Q: Q: P and Q are two coils arranged parallel to each other and coaxially. Q is connected in series with a battery, a closed switch S and a rheostat R. For each of the following situations, show on a sketch, the direction of induced current in P when (a) P is moved closer to Q, (b) Q is moved closer to P, (c) the switch S is open, (d) the sliding contact of the rheostat R is moved to the right. Explain your answers E.m.f. induced in a coil in a changing magnetic field (SB p. 258) Solution

18 © Manhattan Press (H.K.) Ltd. Solution: (a) The current in the coil Q produces a magnetic field which is linked with the coil P. When the coil P is moved closer to Q, the magnetic flux linkage through P becomes greater. By Lenz’s Law, the induced current in P must oppose the increase in magnetic flux linkage through P. So the direction of the induced current in P is opposite to that of the current in Q in order that there is a force of repulsion between the coils. (b) The direction of the induced current in the coil P is the same as that in (a). Whether Q is moved closer to P or P moved closer to Q, the effect is the same, i.e. the coils get closer to each other. Fig. (a) 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 258)

19 © Manhattan Press (H.K.) Ltd. Solution (cont’d): (c) Initially when the switch S is closed, the current through the coil Q produces a magnetic field in the direction as shown in Fig. (b). There is magnetic flux linked with the coil P. When the switch S is open, the magnetic field produced by the coil Q drops to zero, resulting in a change of magnetic flux through P. According to Lenz’s Law, the induced current in P must flow in the direction as shown in Fig. (c) so as to produce a magnetic field opposing the drop in the magnetic flux through P. (d) When the sliding contact of the rheostat R is moved to the right, the rheostat resistance increases. The current through the coil Q decreases. To oppose the decrease in the magnetic flux, the current induced in P must be in the same direction as the initial current through Q as shown in Fig. (d). Fig. (d) Fig. (b)Fig. (c) 17.1 E.m.f. induced in a coil in a changing magnetic field (SB p. 258) Return to Text