Chapter 22
Electromagnetic
Induction
22.4 Faraday’s Law of Electromagnetic Induction
FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION
The average emf induced in a coil of N loops is
) " # "o &
!"
$$ = # N
E = # N ''
E
!t
( t # to %
where, Φ
= BA cos φ
(The motional emf-Φ
relation we derived
is a special case of this.)
the minus sign
reminds us that
the induced emf
will oppose the
change in Φ
 LENZ’S LAW
SI Unit of Induced Emf: volt (V)
Faraday’s law states that an emf is generated if the magnetic flux
changes for any reason. Since Φ = BA cos φ, any change of B, A, or φ
will induce an emf.
22.5 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.
22.5 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
1. Determine whether the magnetic flux that penetrates the coil
is increasing or decreasing.
2. Find what the direction of the induced magnetic field must be
so that it can oppose the change in flux by adding or subtracting
from the original field.
3. Use RHR-2 to determine the direction of the induced current.
22.5 Lenz’s Law
Conceptual Example 8 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.
Since the applied magnetic field in
the loop is increasing and pointing
to the right, Lenz’s law says an
induced current will be created in
the loop to try to oppose this change
by creating an induced magnetic
field to the left.
22.5 Lenz’s Law
Conceptual Example 9 The Emf Produced
by a Moving Copper Ring.
There is a constant horizontal magnetic field
directed into the page in the shaded region.
The field is zero outside the shaded region.
A copper ring is dropped vertically through
the region.
For each of the five positions, determine
whether an induced current exists and, if so,
find its direction.
Is the acceleration of the ring the same as it
drops through the five positions?
Electric generators
A battery converts chemical energy into electrical energy
to produce currents and voltages in circuits.
An electric generator uses Faraday’s Law to convert
mechanical energy into electrical energy.
 Most of the electric power in the world is produced
by electric generators!
(e.g. the 120 V out of your electrical outlet)
22.7 The Electric Generator
HOW AN ELECTRIC GENERATOR PRODUCES AN EMF
An electric generator has essentially the same configuration as an electric
motor, it is just used differently, i.e.,
motor: I  mechanical energy
generator: mechanical energy  I
22.7 The Electric Generator
Equation for the emf, E, induced in a rotating planar coil
For a coil of N loops , loop area, A (valid for any planar shape),
turning at a rotational frequency, f, in a magnetic field, B,
E = NABω sin ωt = E0 sin ωt
ω = 2 πf
angular
frequency in
radians/sec
22.7 The Electric Generator
E = E0 sin ωt ,
E0 = NABω , maximum emf
 emf from generators is sinusoidal in time
 alternating current (ac)
T = period = 1/f = 2π/ω
Example. A generator with a circular coil of 75 turns of area 3.0 x 10-2 m2
is immersed in a 0.20 T magnetic field and rotated with a frequency of
60 Hz. Find the maximum emf which is produced during a cycle.
Solution:
The maximum emf for a generator is
E0 = NABω
We know N = 75, A = 3.0 x 10-2 m2, B = 0.20 T and f = 60 Hz .
Since ω = 2πf = 2π(60) = 377 radians/s
E0 = (75)(3.0 x 10-2)(0.20)(377) = 170 V
22.9 Transformers
A transformer is a device for increasing or decreasing an ac
voltage.
It works on the principle of Faraday’s Law.
Vs
Vp
Vp = -Np ΔΦ/Δt
Dividing Vs by Vp cancels
out ΔΦ/Δt since it is the same 
for the primary and secondary
coils.
Vs = -Ns ΔΦ/Δt
Vs N s
=
Vp N p
Transformer
equation
22.9 Transformers
Vs N s
=
Vp N p
 Vs = (Ns/Np) Vp
Ns > N p  V s > V p
Ns < N p  V s < V p
step-up transformer
step-down transformer
From conservation of energy, the power must be conserved,
Pp = P s  I p V p = I s V s 
I s Vp N p
=
=
I p Vs
Ns
A transformer that steps up the voltage simultaneously steps down the
current, and a transformer that steps down the voltage steps up the current.
Example. A certain transformer has 30 turns in is primary coil and
500 turns in its secondary coil. If a 12 V ac source is attached to the
primary and 4.0 A is flowing in it, find the voltage and current in the
secondary coil.
Solution. Use the transformer equation 
I s Vp N p
=
=
I p Vs
Ns
Vs = (Ns/Np) Vp = (500/30)(12) = 200 V
step-up voltage
Is = (Np/Ns) Ip = (30/500)(4) = 0.24 A
step-down current
Is the power delivered to the secondary coil equal to the power sent
to the primary coil?
Pp = IpVp = (4)(12) = 48 W
, Ps = IsVs = (0.24)(200) = 48 W
16.1 The Nature of Waves
Since we will be studying electromagnetic waves, let’s review some
general features of waves:
1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.
16.1 The Nature of Waves
Longitudinal Wave - the “disturbance” caused by the wave
moves along the direction that the wave propagates,
e.g., sound waves, “compressed slinky waves”……
16.1 The Nature of Waves
Transverse Wave - the “disturbance” caused by the wave moves
perpendicular to the direction that the wave propagates,
e.g., water waves, “shaken slinky waves”, electromagnetic waves….
16.2 Periodic Waves
Periodic waves consist of cycles or patterns that are produced over and
over again by the source.
In the figures, every segment of the slinky vibrates in a simple harmonic
motion, provided the end of the slinky is moved in a simple harmonic
motion.
16.2 Periodic Waves
In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium from
the particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is the number of cycles per time. It is related to the period
and has units of Hz, or s-1.
1
f =
T
16.2 Periodic Waves
The propagation velocity of a periodic wave is related to its frequency and
wavelength. Consider the motion of a long train as a periodic wave which
repeats itself with the passing of each identical car:
Since velocity is
distance/time

!
v = = f!
T