
We have seen



an electric current can experience a force when placed
in a magnetic field
an electric current produces a magnetic field
Obvious question: Can magnetism produce
electricity?

Answer: Yes!

In 1831, Faraday and Henry discovered that a
CHANGING magnetic field can produce an
electric current

A constant/uniform magnetic field does NOT
produce a current
The current I is created only when the magnet moves relative to the coil




A current can also appear in
a coil
of wire in a constant
magnetic field if the
area of
the coil is
changing
The current created by
changing
the field or the coil
area is called
an induced current
When the induced current appears, the coil
behaves as if it had a voltage source called an
induced emf
The process of producing electricity with the aid
of a magnetic field is called electromagnetic
induction

When a conducting rod moves
at
right angles to a constant
magnetic field, the magnetic
force
causes opposite charges
to
appear at the ends of the rod, giving rise to an
induced emf called a motional emf, E
If the rod’s velocity v is constant, the + and –
charges will accumulate until the attractive electric
force FE = q E = q E/L between them becomes
equal in magnitude to the magnetic force FM = q v B
Thus, when equilibrium is reached, E = B L v

The induced emf vanishes when v = 0




Three 1.3-m metal rods move at the same
speed of 2.7 m/s in different planes in a
magnetic field B directed along the +y axis,
as shown. For each rod, find the magnitude
of the motional emf and indicate which end
(1 or 2) is positive. [P22.5]
Answers:


The motional emf will
battery if the
an electric
circuit
act like a
rod is part of
The work done by an external agent to keep the
rod moving is the same as the energy used by
the bulb


A 1.1-m metal rod of negligible resistance is
moving at a speed of 3.3 m/s perpendicularly
to a 0.99-T magnetic field, as in the figure. The
rod is part of a circuit containing a 44-Ω light
bulb. Find (a) the emf induced in the rod, (b)
the current induced in the circuit, and (c) the
energy used by the bulb in 22 s.
Answers:
(a)
 (b)
 (c)

8
The factors relevant to electromagnetic induction
are the magnetic field and the surface area
through which the field passes
 The concept of magnetic flux incorporates both
these factors
 The flux Φ of a magnetic field of magnitude B
through a surface of area A is defined as
Φ = B A cos 
where  is the angle between the field and the
normal to the surface


The SI unit for magnetic flux is weber (Wb),
where 1 Wb = 1 tesla·meter2
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
9


The magnetic flux is proportional to the number
of field lines that
pass through a
surface
The flux is largest when
0, and vanishes
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
=
when
 = 90°


A house has a floor area of 112 m2 and an outside
wall having an area of 28 m2. The earth magnetic
field here has a horizontal component of 2.6×10–5 T
pointing due north and a vertical component of
4.2×10–5 T pointing straight down, toward the
earth. Find the magnetic flux through the wall if it
faces (a) north and (b) east. (c) What’s the flux
through the floor? [P22.11]
Answers:



(a)
(b)
(c)

The motional emf is related to the time rate of
change of the magnetic flux by
 x - x0  B A - B A0  - 0 
EB L



t - t0
t - t0
t
 t - t0 
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
12


How electromagnetic induction occurs in general
is summarized by Faraday’s law of
electromagnetic induction
This law states that the average emf E induced
in a coil of N loops is related to the change 
in magnetic flux through one loop and the time
interval t during which the change occurs by
  - 0 

E  N 
  N
t
 t - t0 



Since Φ = B A cos , the flux change
 occurs when B, A, , or two of
them, or all of them change
Thus the emf E is induced when any
one or more of B, A, and  change
Note that motional emf is a special
case of induced emf


A flat coil of wire having 55 turns and an area
of 0.11 m2 is initially oriented so the normal of
its surface is parallel to a constant magnetic
field of magnitude 0.77 T. The coil is then
rotated through an angle of 60.0° in 0.10 s. (a)
Find the average induced emf. (b) What would
be the induced emf if the coil were returned to
its initial
orientation in
the
same time of
0.10 s?
Answers:


(a)
(b)


A magnetic field is perpendicular to a 0.040-m
× 0.060-m rectangular coil of wire having 100
turns. In a time of 0.050 s, an average emf of
magnitude 1.5 V is induced in the coil. What is
the magnitude of the change in the magnetic
field?
Answer:




An induced emf drives the induced current around a
circuit just as a battery voltage does a conventional
current
Note that an induced current produces a new field
called the induced magnetic field
How to determine the polarity (the + and –
terminals) of the induced emf is summarized by
Lenz’s law
This law states that 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



Example
Determine whether the magnetic flux through
a coil
is increasing or decreasing
Find what the direction of
the
induced magnetic field
must be, so
that it can
OPPOSE the CHANGE in
flux
by adding to or subtracting
from the original field
Use RHR-2 to determine the
direction of the induced
current and
hence the
polarity of the induced
emf


A constant magnetic field
directed into the page exists in
the rectangular regions shown
in the figure
As the ring slides through the
region, from position 1 to
position 5, an induced current
is induced at locations 2 and 4
19

SAT 22.1.3

SAT 22.1.4

SAT 22.1.5

SAT 22.1.7

SAT 22.1.8

SAT 22.1.9
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
20

A device that converts mechanical work into
electrical energy is called a generator



It does just the opposite of what a motor does
The mechanical work is done by a person, wind,
falling/flowing
water, etc.
Some hybrid
have
act as generators
vehicles
motors that can

A generator having a coil with N loops, each of
area A, that rotates in a constant magnetic field
of magnitude B, produces an ac emf given by
E = N A B ω sin (ωt) = E0 sin (ωt)
where E0 is the peak emf, and ω is the angular
speed of the coil, related to the frequency f by
ω=2πf


Such a generator is also
called an ac generator
Simulation


A generator using a coil with 150 turns,
each having an area of 0.020 m2, produces
the emf as a function of time shown in the
figure. Find (a) the angular speed of the coil
and (b) the magnitude of the magnetic field.
Answers:


(a)
(b)



A CHANGING current in
a coil of wire produces
a CHANGING magnetic
field around it
Another coil placed
near the 1st coil “feels”
a CHANGING magnetic flux through it and,
consequently, an emf is induced in the 2nd coil
The effect in which a changing current, Ip, in the
primary (coil) induces an emf in the secondary
(coil) is called mutual induction
If the secondary has Ns loops, and Φs is the flux
through 1 loop, the total flux through the secondary
is Ns Φs, which is proportional to the current Ip in
the primary, or
Ns Φs = M Ip
where M is a constant called the mutual inductance
of the 2 coils
 The average emf Es induced in the secondary by a
change in current Ip in the primary during a time t
is
Ip


Es  Ns

s
t
 M
t
The SI unit for inductance is henry (H) where 1 H =
1·V s/A


During a 72-ms interval, a change in the
current in a primary coil occurs. This change
leads to the appearance of a 6.0-mA current in
a nearby secondary coil. The secondary is part
of a circuit having a resistance of 12 Ω. The
mutual inductance between the 2 coils is 3.2
mH. What is the change in the primary
current? [P22.49]
Answer:


An emf can be induced in a current-carrying coil
by a change in the magnetic field that the current
itself produces
The effect in which a changing current in a
circuit induces
an
emf in the
same circuit
is
called selfinduction
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
28
If a coil has N loops, and Φ is the flux through 1
loop, the total flux through the coil is N Φ,
which is proportional to the current I in the coil,
or
NΦ=LI
where L is a constant called the self-inductance, or
simply inductance, of the coil
 The average emf E induced in the coil by a current
change I in the same coil during a time t is


I
E  N
 L
t
t

The – sign implies E opposes I




Because of their self-inductance, coils are also
called inductors
An inductor, like a capacitor, can store energy
Since work must be done to create
a current
in an inductor, energy is stored in it once a
current I is established in it
The energy in a coil of inductance L is
energy = ½ L I2


A solenoid has a 3.1-H inductance and initially
carries a 15-A current. (a) If the current goes from
15 to 0 A in a time of 75 ms, what is the emf
induced in the solenoid. (b) What is the amount of
electrical energy stored initially in the solenoid? (c)
At what rate must the energy be removed from the
solenoid when the current is reduced to zero in 75
ms? [P22.79]
Answers:
 (a)
 (b)
 (c)

A transformer is a device for increasing or
decreasing an ac voltage


based on the idea of (mutual) induction
consisting of a primary coil with Np turns and a
secondary coil with Ns turns, both wound on an iron
core
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
32

Transformers



operate with ac electricity, not with dc
play a key role in transmitting electric power from
power plants to consumers
A step-down (step-up) transformer decreases
(increases) a voltage


The iron core causes the 2 coils to have (nearly) the
same flux Φ
The voltages Vp & Vs across the primary & secondary,
respectively, are related byVthe transformer
equation
N
s
Vp


s
Np
Thus a step-down (step-up) transformer has
Ns/Np < 1 (Ns/Np > 1)

Simulation

If the transformer is 100% efficient,
23,26,28,30 Mar 2007
PHYS 202: Chapter 22
Is
Ip

Np
Ns34


A transformer inside a table lamp has 330
turns in the primary and 25 turns in the
secondary. When the primary is connected
to a 120-V outlet, there is a current of 11 A
in the secondary. Find (a) the current in the
primary and (b) the average power
delivered to the
bulb.
Answers:


(a)
(b)