1. Electromagnetic Induction
Chapter 23
Electromagnetic Induction

2. Recall Electric Flux: FE = EAcosq
Magnetic Flux
F = BAcosq
Three ways to change the Magnetic FluX:
Change B
Change A
Change q

3. Induced Emf and Induced Current
There are a number of ways a magnetic field can be used to
generate an electric current.
It is the changing field that produces the current.

4. Induced Emf and Induced Current
The current in the coil is called the induced current because it is brought
about by a changing magnetic field.
Since a source emf is always needed to produce a current, the coil behaves
as if it were a source of emf. This emf is known as the induced emf.

5. Induced Emf and Induced Current
An emf can be induced by changing the
area of a coil in a constant magnetic field
In each example, both an emf and a current are induced because
the coil is part of a complete circuit. If the circuit were open, there
would be no induced current, but there would be an induced emf.
The phenomena of producing an induced emf with the aid of a
magnetic field is called electromagnetic induction.

6. THE EMF INDUCED IN A MOVING CONDUCTOR
22.2 Motional Emf
THE EMF INDUCED IN A MOVING CONDUCTOR
Each charge within the conductor
is moving and experiences a
magnetic force
The separated charges on the
ends of the conductor give rise
to an induced emf, called a
motional emf.

7. Motional emf when v, B, and L are mutually perpendicular

8. Operating a Light Bulb with Motional Emf
Suppose the rod is moving with a speed of 5.0m/s
perpendicular to a 0.80-T magnetic field. The rod
has a length of 1.6 m and a negligible electrical
resistance. The rails also have a negligible
electrical resistance. The light bulb has a
resistance of 96 ohms. Find (a) the emf produced
by the rod and (b) the current induced in the
circuit.

9. Motional Emf
(a)
(b)

10. MOTIONAL EMF AND ELECTRICAL ENERGY
In order to keep the rod moving at constant velocity, the force
the hand exerts on the rod must balance the magnetic force on
the current:

11. Conservation of Energy A conducting rod is free to slide down between
Motional Emf
Conservation of Energy
A conducting rod is free to slide down between
two vertical copper tracks. There is no kinetic
friction between the rod and the tracks. Because
the only force on the rod is its weight, it falls with
an acceleration equal to the acceleration of
gravity.
Suppose that a resistance connected between the
tops of the tracks. (a) Does the rod now fall with
the acceleration of gravity? (b) How does the
principle of conservation of energy apply?

13. MOTIONAL EMF AND MAGNETIC FLUX

14. Magnetic Flux

15. GENERAL EXPRESSION FOR MAGNETIC FLUX

16. Magnetic Flux

17. GRAPHICAL INTERPRETATION OF MAGNETIC FLUX
The magnetic flux is proportional
to the number of field lines that pass
through a surface.

18. Faraday’s Law of Electromagnetic Induction
The average emf induced in a coil of N loops is
SI Unit of Induced Emf: volt (V)

19. `Faraday’s Law of Electromagnetic Induction
The Emf Induced by a Changing Magnetic Field
A coil of wire consists of 20 turns each of which has an area of m2.
A magnetic field is perpendicular to the surface. Initially, the magnitude of
the magnetic field is T and 0.10s later, it has increased to T.
Find the average emf induced in the coil during this time.

20. For the 20 – loop circuit shown below, compute the EMF Induced by the changing
Magnetic Flux due to the magnetic field B = 2.50 t3 k at to =10.0 s.

22. The induced emf resulting from a changing magnetic flux has a
Lenz’s Law
LENZ’S LAW
The induced emf resulting from a changing magnetic flux has a
polarity that leads to an induced current whose direction is such
that the induced magnetic field opposes the original flux change.

23. The induced emf resulting from a changing magnetic flux has a
Lenz’s Law
LENZ’S LAW
The induced emf resulting from a changing magnetic flux has a
polarity that leads to an induced current whose direction is such
that the induced magnetic field opposes the original flux change.
Reasoning Strategy
Determine whether the magnetic flux that penetrates the coil
is increasing or decreasing.
Find what the direction of the induced magnetic field must be
so that it can oppose the change influx by adding or subtracting
from the original field.
3. Use RHR-2 to determine the direction of the induced current.

24. The Emf Produced by a Moving Magnet
Lenz’s Law
The Emf Produced by a Moving Magnet
A permanent magnet is approaching a
loop of wire. The external circuit consists
of a resistance. Find the direction of the
induced current and the polarity of
the induced emf.

25. There is a constant magnetic field directed
Lenz’s Law
The Emf Produced
by a Moving Copper Ring.
There is a constant magnetic field directed
into the page in the shaded region. The field
is zero outside the shaded region. A copper
ring slides through the region.
For each of the five positions, determine whether
an induced current exists and, if so, find its
direction.

26. The Electric Generator
HOW A GENERATOR PRODUCES EMF

27. The Electric Generator

28. The Electric Generator
Emf induced in a rotating planar coil

29. The Electric Generator

31. Example 23.5 Electric Field Induced by a Changing Magnetic Field in a Solenoid
A long solenoid of radius R has n turns of wire per unit length and carries a time-varying current that varies sinusoidally as I = Imax cost, where Imax is the maximum current and v is the angular frequency of the alternating current source.

32. Example 23.5 Electric Field Induced by a Changing Magnetic Field in a Solenoid
(A) Determine the magnitude of the induced electric field outside the solenoid at a distance r > R from its long central axis.
Evaluate the right side of the general form of Faraday’s law of induction:
Evaluate the magnetic field in the solenoid:

33. Example 23.5 Electric Field Induced by a Changing Magnetic Field in a Solenoid
Substitute:
Evaluate:
Solve for the magnitude of the electric field:

34. Example 23.5 Electric Field Induced by a Changing Magnetic Field in a Solenoid
(B) What is the magnitude of the induced electric field inside the solenoid, a distance r from its axis?
Evaluate the right side of the general form of Faraday’s law of induction:
Substitute Equation (2) into Equation (5):

35. Example 23.5 Electric Field Induced by a Changing Magnetic Field in a Solenoid
Substitute Equations (4) and (6) into Faraday’s law equation:
Solve for the magnitude of the electric field:

36. Consider a flat square coil with N = 5 loops
Consider a flat square coil with N = 5 loops. The coil is 20 cm on each side, and has a magnetic field of 0.3 T passing through it. The plane of the coil is perpendicular to the magnetic field: the field points out of the page.
The magnetic field is increased uniformly from 0.3 T to 0.8 T in 1.0 seconds. While the change is taking place, what is the induced emf in the coil?
While the magnetic field is changing, the emf induced in the coil causes a current to flow. Does the current flow clockwise or counter-clockwise around the coil?
Current must flow clockwise around the loop

37. A transformer is a device for increasing or decreasing an ac voltage.
Transformers
A transformer is a device for increasing or decreasing an ac
voltage.

38. Transformers
Transformer
equation

39. A transformer that steps up the voltage simultaneously steps
Transformers
A transformer that steps up the voltage simultaneously steps
down the current, and a transformer that steps down the voltage
steps up the current.

40. Transformers

43. Transformers
A transmission line delivers power at a potential of 300 kV to a transformer
designed to step to 8kV. If the primary coil has turns how many turns
should the 2nd coil have? If the transmission delivers 500 A what is the current
at the secondary?

44. Power output by a power plant is 100 MW to 1 GW.
P output = VI. P lost = I2 R cable

45. A transmission line delivers power at a potential of
The primary of a transformer is connected to a source of voltage that has two components: an alternating current (AC) component of 120 volts and a steady direct current (DC) component of 5 volts. The number of turns of the primary is 300 and the that of the secondary is What is the voltage at the output of the secondary?

46. Melting a nail R of nail = 0.001 Ohms.
Use a 100 – to – 1 step-down transformer

47. Electromagnetic Waves
Chapter 24
Electromagnetic Waves

48. The Nature of Electromagnetic Waves
Two straight wires connected to
the terminals of an AC generator
can create an electromagnetic
wave.
Only the electric wave traveling to the
right is shown here.

49. The Nature of Electromagnetic Waves
The current used to generate
the electric wave creates a
magnetic field.

50. The Nature of Electromagnetic Waves
This picture shows the wave of the radiation field far from the
antenna.
The speed of an electromagnetic wave in a vacuum is:

51. An oscillating electric field generates an oscillating magnetic field.
An oscillating magnetic field generates an oscillating electric field.

52. 24.3 Electromagnetic Waves
An electromagnetic wave consists of oscillating electric and magnetic fields
The changing fields induce each other, which maintains the propagation of the wave
a changing electric field induces a magnetic field
a changing magnetic field induces an electric field

53. The Electromagnetic Spectrum
Like all waves, electromagnetic waves have a wavelength and
frequency, related by:

54. The Electromagnetic Spectrum
Example 1 The Wavelength of Visible Light
Find the range in wavelengths for visible light in the frequency range
between 4.0x1014Hz and 7.9x1014Hz.

55. The Electromagnetic Spectrum
The Diffraction of AM and FM Radio Waves
Diffraction is the ability of a wave to bend around an obstacle or the
edges of an opening. Would you expect AM or FM radio waves to
bend more readily around an obstacle such as a building?
AM waves are much longer than FM waves and waves tend to bend easier
around objects (i.e. diffract) when the object’s size is on the
order of or less than the size of the wavelength. It is found
that AM waves bend easier around buildings and hills than FM waves.

56. The Speed of Light
The speed of light
in a vacuum

57. Maxwell’s prediction of the speed of light

58. Conceptual Example 3 Looking Back in Time
The Speed of Light
Conceptual Example 3 Looking Back in Time
A supernova is a violent explosion that occurs at the death of certain
stars. The figure shows a photograph of the sky before and after a
supernova. Why do astronomers say that viewing an event like this
is like looking back in time?

59. The Energy Carried by Electromagnetic Waves
The total energy density carried by an electromagnetic
wave

60. The Doppler Effect and Electromagnetic Waves
Electromagnetic waves also can exhibit a Dopper effect, but it
differs for two reasons:
Sound waves require a medium, whereas electromagnetic
waves do not.
For sound, it is the motion relative to the medium that is important.
For electromagnetic waves, only the relative motion of the source
and observer is important.
where v is the relative speed between the source and the observer,
c is the speed of light,
f is the frequency of light detected by the observer,
and f is the frequency emitted by the source.

61. The Doppler Effect and Electromagnetic Waves
A speceship is moving towards the police car at a speed of 1.5 × 108 m/s.The spaceship flashes the headlight on john of frequency 4200 Hz. At what frequency will you receive the light?
2100 Hz

62. POLARIZED ELECTROMAGNETIC WAVES
Polarization
POLARIZED ELECTROMAGNETIC WAVES
Linearly polarized wave
on a rope.

63. In polarized light, the electric field
Polarization
In polarized light, the electric field
fluctuates along a single direction.

64. Polarized light may be produced from unpolarized light with
Polarization
Polarized light may be produced from unpolarized light with
the aid of polarizing material.

65. MALUS’ LAW intensity before intensity after analyzer analyzer
Polarization
MALUS’ LAW
intensity before
analyzer
intensity after
analyzer

66. When Polaroid sunglasses are crossed, the intensity of the
24.6 Polarization
When Polaroid sunglasses are
crossed, the intensity of the
transmitted light is reduced to
zero.