1. Electromagnetic Induction
Chapter 28

2. What is Electromagnetic Induction?
Whenever the magnetic field passing through a coil changes an emf appears in the coil. This is Electromagnetic Induction.

3. To Demonstrate Electromagnetic Induction
Move the magnet towards (or away from) the coil.
The galvanometer deflects, indicating that current flows and that an emf appears.
When the magnet is not moving the meter reads zero.

4. Another example of Electromagnetic Induction
When switch S in circuit A is closed the meter in circuit B gives a deflection.
When the switch remains closed, causing a steady current in circuit A, no current flows in circuit B.
If the switch is now opened the meter deflects, but in the opposite direction.

5. A Further Example of Electromagnetic Induction
Alternating Current flows in coil 1.
The meter connected to coil 2 is a meter that reads a.c.
The meter will indicate that a current always flows in coil 2.

6. What is Magnetic Flux? Magnetic flux  is defined as:  = B A Where:
B = magnetic flux density
A = area
Magnetic flux through Area A is equal to
Magnetic Flux Density × Area

7. What is the SI Unit of Magnetic Flux?
The SI Unit of Magnetic Flux is the weber (Wb).
Magnetic flux is a Scalar Quantity.

8. B = 3 T
What is the magnetic flux through a loop of area
0.5 m2 placed at right angles to a magnetic field of flux density 3 T?
 = B A
= (3)(0.5)
= 1.5 Wb
A = 0.5 m2

9. What if the magnetic field is not perpendicular to the area?
Resolve the magnetic flux density B into components parallel and perpendicular to the area.
Flux through A =
Component of B perp to A × (area A)
In the diagram :
Component of B perp. to coil
= B Sin 30o = 2 Sin 30o = 1 T
Flux through coil = B × A
= (1)(0.4) = 0.4 Wb

10. State Faraday’s Law of Electromagnetic Induction.
Faraday’s Law states that the induced emf is directly proportional to the rate of change of magnetic flux.

11. Experiment to demonstrate Faraday’s Law of Electromagnetic Induction
Move the magnet towards the coil slowly.
The galvanometer gives a small deflection, indicating a small induced emf.
Move the magnet towards the coil quickly.
The galvanometer gives a large deflection, indicating a large induced emf.
Conclusion: The induced emf is directly proportional to the rate of change of magnetic flux through the coil.

12. State Lenz’s Law.
Lenz’s Law states that the induced current flows in such a direction as to oppose the change causing it.
Lens’s law follows from the
Principle of Conservation of Energy.

13. As the man runs towards a coil the magnetic flux through the coil increases. An emf is induced in the coil.
By Lenz's Law the current induced in the coil flows in a direction that opposes the north pole of the magnet approaching.
The current flows in a direction that causes the end of the coil facing the approaching magnet to behave like a north pole (north repels north).
Because of this opposition the man must do work to bring the magnet nearer the coil. The work he does appears as electrical energy in the coil.

14. As the man runs away from the coil the direction of the induced current changes so that his motion is still opposed.
The direction of the induced current changes so that a south pole appears at the right hand side of the coil (south attracts north).
The work the man does in pulling a north pole away from a south pole again appears as electrical energy in the coil.

15. Experiment to demonstrate Lenz’s Law
Hang a light aluminium ring from a piece of thread.
Move the north pole of a bar magnet quickly towards the ring.
The ring moves away from the magnet.
Move the north pole quickly away from the ring and the ring follows the magnet.
Conclusion: As the north pole approaches current is induced in the ring. A north pole appears at the side of the ring nearest the magnet. The magnet repels it and the ring moves away.
When the north pole is taken away the direction of the induced current changes, a south pole appears at the side of the ring facing the magnet. The ring is attracted to the magnet and follows it.
This agrees with Lenz’s Law and thus the law is demonstrated.

16. Experiment to demonstrate Lenz’s Law
Drop a metal cylinder through a copper pipe. Note how long it takes to fall through the pipe.
Drop a strong cylindrical magnet (same size and weight as the metal cylinder) through the copper pipe. It takes much longer to fall through.
As the magnet falls through the pipe, its changing magnetic field induces currents in the pipe. By Lenz’s Law these currents flow in such a direction as to oppose the change producing them, i.e the moving magnet. They exert forces on the magnet slowing it down. The non magnetic metal cylinder does not experience these forces
Thus Lenz’s Law is demonstrated.

17. What is an Electric Generator?
An Electric Generator is a device that converts mechanical energy into electrical energy.
The alternator in a car is an electrical generator. This one has a maximum power output of 1 kW.

18. Electric Generators
Electromagnetic Induction is the principle on which the Electric Generator is based.
In an electricity generating station some form of energy e.g. chemical energy from coal or oil is used to produce steam which causes a turbine to rotate - i.e. the turbine is given kinetic energy.
The turbine rotates a coil in a magnetic field thereby causing the magnetic flux through it to change and an emf is induced in it.
Thus the kinetic energy is converted to electrical energy.

19. Everyday examples of Electric Generators
Electricity Power Stations which generate huge quantities of electricity.
The Alternator in a Car is turned by the engine and generates electricity to supply power to the car’s electrical system to continually keep the car battery charged.
The Dynamo on a bicycle generates electricity to operate the bicycle’s lights.

20. What is alternating Current (a.c.)?
An electric current that periodically reverses the direction in which it flows is called Alternating Current (a.c.).
The current that flows through an ordinary domestic light bulb when connected to the mains electricity supply reverses direction 100 times every second.
Mains Electricity is alternating current.

21. Alternating Current
A Graph of Current against Time for alternating current

22. Alternating Voltage
To produce alternating current an alternating voltage is needed.
The diagram shows a graph of an a.c. voltage against time on an oscilloscope.
If alternating voltage is applied across a pure resistor the current flowing at any instant is found from Ohm's Law.

23. Alternating Voltage
Graph of Voltage against Time for A.C.
Voltage / V

24. A.C. and Heating
3 A d.c. flows in a 6  resistor. Heat is produced in the resistor at a rate given by Joule's Law: P = I 2R = (3)2(6) = 54 J s-1
If Alternating Current flows in the resistor what is the maximum value of the a.c. if it produces heat at the same rate as the 3 A d.c.?
Clearly if the a.c. only reaches 3 A in each direction it will not produce heat at the rate of 54 J s-1, because the current is less than 3 A at all other times in each cycle.

25. rms Value of an Alternating Current (or Voltage)
When we state that the value of an Alternating Current is 5 A, we mean that this alternating current has the same heating effect as a 5 A direct current.
Since alternating current varies with time, to have the same heating effect as a 5 A d.c. it must have a maximum value in each direction which is greater than 5 A.
The stated value of an alternating current is called its rms value ( symbol Irms ).
The Maximum or Peak Value of the current is symbolised: I0

26. It can be shown that: The same thing applies to alternating voltages:
and
The same thing applies to alternating voltages:
and

27. Peak voltage (V0) and rms Voltage (Vrms)
The peak voltage of the mains electricity in Europe is 325 V. Calculate the rms voltage of the mains.
Mains voltage is supplied at an rms value of 110 V in the US. Calculate the peak value of the voltage.

28. What is Mutual Induction?
If a changing electric current in one coil causes an induced emf to appear in a nearby coil there is said to be Mutual Inductance between the two circuits.

29. How can the amount of Mutual Induction between two coils be increased?
Move the coils nearer each other.
Wind the coils on the same soft Iron core.
Increase the number of turns on either or both of the coils.
Mutual inductance occurs in the Transformer and the Induction Coil.

30. Experiment to show Mutual Induction
When the switch S is opened (or closed) the current in coil 1 changes and thus the magnetic field around it changes. This changing magnetic field passes through coil 2.
As this happens the galvanometer in coil 2 gives a deflection showing that an emf is induced in coil 2.
There is thus mutual inductance between the two coils.

31. What is Self Induction?
Whenever the current passing through a coil changes the magnetic field surrounding that coil changes.
This changing magnetic field induces an emf in the coil that opposes the changing current. (This emf is called a back emf ).
This phenomenon is called Self Induction.

32. Experiment to demonstrate Self Induction
When the switch is closed the bulb does not light immediately. It takes a number of seconds for the bulb to reach full brightness.
This is due to the self inductance of the coil.

33. Explanation of the Experiment to demonstrate Self Induction
When the switch is closed the current starts to flow and immediately produces a magnetic field around the coil. This field is increasing.
Since the coil now has a changing magnetic field in it, by Faraday's Law an emf will be induced in the coil.
By Lenz's Law the direction of the emf opposes the change producing it, i.e. it opposes the increasing current.
The induced emf opposes but does not succeed in preventing the current from increasing. Such an emf is called a Back emf.

34. The Effect of an Inductor on a.c.
A 12 V battery sends a 2 A d.c current through a 6 Ω resistor.
If a 12 volt a.c. source (Vrms = 12 V) is connected to a coil of resistance 6  with a soft Iron core in it, current still flows.
However the current that now flows, is much less than 2 A. The reason is:
Alternating current continually changes and so the magnetic field around the coil also changes. By Faraday's and Lenz's Laws an emf is induced in the coil that always opposes the changing current.
It is this back emf that causes the coil to offer more opposition to a.c. than to d.c.

35. A filament lamp lights when connected in series with an a. c
A filament lamp lights when connected in series with an a.c. power supply and a coil. Explain why the lamp goes out when a soft Iron core is inserted into the coil.
The core causes an increased magnetic flux in the coil and hence a greater rate of change of magnetic flux.
A coil carrying a.c. has a back emf. The greater rate of change of magnetic flux causes the back emf to increase.
This reduces the net voltage and the current decreases. The lamp goes out because the current decreases.

36. A.C. and Inductors
A coil (an inductor) opposes the flow of direct current (d.c.) with its Ohmic Resistance.
A coil (an inductor) opposes the flow of alternating current (a.c.) with its Ohmic Resistance and the Back emf Induced in it.

37. A Dimmer Switch

38. What is a Transformer?
A Transformer is a device used to change the value of an Alternating Voltage.

39. Structure of a Transformer
A Transformer consists of two coils of wire wound on a soft Iron core.
One coil, called the Primary Coil has an alternating voltage, called the Input Voltage, applied to it.
The transformer causes a different voltage to appear across other coil, called the Secondary Coil.
The voltage across the secondary coil is the Output Voltage.

40. How a Transformer Operates
The Input Voltage ​V​i​ across the primary coil causes alternating current in the primary coil.
This current causes an alternating magnetic flux in the Iron core.
This alternating flux passes through the secondary coil and induces an emf ​V​o in it. V​o is the Output Voltage.
The size of the Output Voltage, ​V​o, depends on the number of turns in the secondary ​N​s​ and ​N​p​, the number of turns on the primary coil.

41. Transformer Formula Vi = Input Voltage = Voltage across Primary Coil
Np = Number of Turns on Primary coil
Vo = Output Voltage = Voltage across Secondary Coil
Ns = Number of Turns on Secondary Coil

42. If Ns is greater than Np then Vo is greater than Vi and it is called a Step Up Transformer.
If Ns is less than Np then Vo is less than Vi and it is called a Step Down Transformer.

43. To Demonstrate the Action of a Transformer
With an a.c. voltmeter measure the voltage across the primary coil and the emf across the secondary coil.
It will be seen that if Ns > Np then Vo > Vi and vice versa.
By noting the number of
turns on each coil the formula:
can be verified

44. A charged Capacitor Blocks Direct Current (d.c.)
A Capacitor Conducts Alternating current (a.c.)