1. Electromagnetic Induction

2. Magnetic Flux The magnetic flux is important in understanding electromagnetic induction. The magnetic flux (Φ) is a measure of the number of field lines passing through a region. The unit of magnetic flux is the weber (W) It is a vector quantity In a uniform field the number of field lines passing through the larger region B is greater than through the smaller region A. Therefore we can say that there is a greater flux through B than A A B A uniform magnetic field has a constant density of field lines throughout

3. Magnetic Flux Here the magnetic flux is the same in region A and B. Sometimes a measure of magnetic flux can be misleading.

4. Magnetic Flux Below the magnetic flux through region A is greater than through B because the density of the field lines is greater. A B

5. The relationship between B and Φ A B If the magnetic field is perpendicular to a region with area A, and the flux density is B, Then the flux Φ in that region is given by: Φ = AB

6. Moving a conducting wire in a magnetic field If a wire is moved in a magnetic field such that field lines are cut an emf is induced between the ends of the wire N SS N An emf is induced between the ends of the wire An emf is NOT induced between the ends of the wire

7. N S Direction of induced emf The direction of the induced emf field emf motion

8. Induced e.m.f and moving electrons Motion of the bar Magnetic field Force tends to move electrons in this direction As we saw with free electrons moving in a field, they experience a force as show in the diagram ------ +++ ++ Here we see that conventional current will be driven from C to A if the circuit is complete. i.e. the direction of the emf is from C to A. C A C A

9. N S The direction of the induced emf With a closed conducting loop, the emf induced drives a current through the loop

10. N Here a current is induced in the single turn coil in the same way. If a current flows it always produces a field which opposes the motion of the coil. In this case a north pole is induced on the face of the coil being pulled towards the magnet. This is a consequence of the law of conservation of energy. It always applies. It is known as Lenz’s law.

11. N Again as a consequence of Lenz’s law When the coil is withdrawn a south pole is produced to oppose the motion of the coil. Note that if a North pole had been produced instead, the coil would be repelled and the current due to induction increased. This would cause further repulsion. We would have built a perpetual motion machine! We would get energy for nothing in contravention of the law of conservation of energy.

12. N Coils With More Turns A AA When a magnet moves through the coil, each turn of the coil cuts the magnetic field by the same amount. So the flux linkage is just the sum of flux through each turn. If the magnet is moved with the same speed. 2 turns, → 2 x emf 3 turns → 3 x emf etc. Where the coil has more than one turn, the magnetic flux through the turns of the coil is called the flux linkage.

13. S N AA G North pole induced at the top of the coil on approach North pole induced at the bottom of the coil on leaving

14. S N A V Induced emf/V Time/s The direction of the emf is reversed as the induced poles of the coil are reversed. The bar magnet is accelerating so the rate of flux cutting is higher as the magnet leaves the coil, hence the larger amplitude of emf for a shorter time.

15. Faraday’s Law of Electromagnetic Induction 1.The e.m.f. induced in a coil depends on the rate of change of flux through the coil. N The faster the flux changes the greater the e.m.f. induced

16. N Faraday’s law of electromagnetic induction The e.m.f. induced is proportional to the number of turns in the coil N

17. Faraday’s law of electromagnetic induction So combining these relationships The units of the SI system combine in such a way that the constant of proportionality is 1 The expression to the right of the = sign is just the rate of change of flux linkage

18. Faraday’s Law E is the e.m.f. Induced (V) N is the number of turns on the coil ∆Φ is the change in flux though each turn of the coil. (Wb) ∆t is the time taken for the flux change.(s) Note that in this equation the total change in flux linkage in the coil is N∆Φ. Sometimes you may see this written as ∆NΦ. It follows that 1 weber is the flux linkage in a coil if an emf of 1V falls evenly to zero in 1 second

19. Using Faraday’s Law A coil of 200 turns and 3cm in radius lies perpendicular to a uniform magnetic field with a flux density of 2 x10 -2 T. The field falls evenly to 0T in 1s. Calculate the emf generated:. V 1.Calculate the flux through 1 turn of the coil 2 Now apply Faraday’s law

20. Some effects of induction

21. The effect of a changing field on an aluminium ring d.c. supply to coil When the d.c. supply is switched on, there is a change in flux through the aluminium ring. An emf is induced in the ring with a field opposed to the coil. The ring is repelled and rises. As soon as the current is steady though the coil there is no further change in flux and the ring falls back. When the circuit is broken, the flux changes again through the ring and the ring is repelled again in accordance with Lenz’s law.

22. The effect of a changing field on an aluminium ring ac. supply to coil When the a.c. supply is switched on, there is a continuous change in flux through the aluminium ring. An emf is induced in the ring with a field opposed to the coil. This field reverses every time the field in the coil reverses.The ring continues to be repelled.

23. Electromagnetic damping

27. When the coil L is connected in series with the cell V it produces an increasing magnetic field as the current through the coil rises. This induces a “back emf” in the reverse direction to the emf produced by the cell. The magnetic field stores energy transferred from V When S is moved so that L is in series with R only, the back emf drives a current through R dissipating the energy stored. BACK EMF