Download Chapter 22 Electromagnetic Induction

Chapter 22
Electromagnetic
Induction
When a coil of wire is in
a magnetic field, the
magnetic flux Ф is the
strength of the field B
multiplied by the area
of the coil A, Ф = BA.
A potential difference is produced
whenever the magnetic flux Ф is
changed. This potential difference
is in the form of an induced emf ε
and is equal to the rate of change
in magnetic flux, the magnetic flux
divided by the time, ε = ΔФ/Δt or
ε = ΔBA/Δt. This is Faraday’s Law
of Induction.
Since flux is BA anything
that changes B or A will
produce an emf. (1) If the
strength of the magnetic
field is changed, the flux
changes and a potential
difference is produced.
(2) Area in the field can be
changed by moving a coil of
wire into or out of a magnetic
field. Area in the field can also
be changed by rotating a coil of
wire about its diameter if the
diameter is perpendicular to the
field.
Example 1: A loop of wire of
2
area 0.11 m is in a 1.0 T
magnetic field. If the field
strength increases to 4.0 T
over a period of 5 seconds,
what emf is produced?
Example 2: A loop of wire of
area 0.5 m2 is moving into a
0.7 T magnetic field. If it
takes 4 seconds for the loop
to move from completely
outside the field to completely
inside the field, what emf is
produced?
When an emf is produced using
Faraday’s Law a current can be
produced. This current will
produce its own magnetic field
as discussed in the previous
chapter. But, what is the
direction of the original emf and
the conventional current flow?
The direction is such that the
magnetic field it produces is
opposite the change in flux that
produces the emf. This is Lenz’s
Law and it is how the direction of
the induced current is found.
(ε = ΔФ/Δt is usually written with a
minus sign, ε = -ΔФ/Δt, to indicate
the emf and the current produced
are opposite the change in flux.)
To find the direction of the
induced current, first determine
if the change in flux ΔФ or ΔBA
is an increase or a decrease. If
it is an increase, the magnetic
field produced by the induced
current must be in the opposite
direction of the original
magnetic field.
If the change in flux is a decrease,
the magnetic field produced by the
induced current must be in the
same direction as the original
magnetic field. Once the direction
of the field produced is known, right
hand rule two, rhr-2, is used to find
the direction of the induced current
produced.
Example 3: A permanent magnet approaches a
loop of wire. The external circuit attached to the
loop consists of the resistance R. Find the direction
of the induced current and the polarity of the
induced emf.
Example 4: A conductive loop is entering a
magnetic field directed into the plane of the
paper. Is the direction of the current
produced in the loop clockwise or
counterclockwise?
Example 5: This loop continues until it
leaves the field. Is the direction of the
current produced in the loop clockwise
or counterclockwise?
Example 6: What is the direction of
the current produced in the loop
when it is completely inside the
field?
The picture above depicts a
counterclockwise current flow
produced by change in the magnetic
field. Is the magnetic field increasing
or decreasing?
An electric generator rotates a coil of wire in
a magnetic field. As we have previously
seen, this produces an emf in the wire coil
and therefore a flow of current. The nature of
this rotation causes the direction of the
current produced to alternate directions. This
is how the AC we use in our homes is
produced. It is also how the alternator in
your car produces the current to run the
electrical devices in the car and recharges
the car’s battery.
As we saw last chapter, there is
a force on a wire carrying a
current in a magnetic field
(F= I l B). An electric motor uses
this force to produce motion.
But Lenz’s Law tells us that this
motion of a coil of wire through
the magnetic field also produces
an induced current.
By Lenz’s Law the emf produced is
opposite the direction of the emf
that produces the current that turns
the motor. Since it is opposite the
direction of the source potential this
induced emf is called back emf.
The net potential difference across
the motor is the potential of the
source minus the back emf.
Example 7: A motor is
connected to a 120 V source.
The resistance in the motor
coil is 10 Ω and the current
produced by the back emf is
11 A. What is the net
potential across the motor?
Have you ever wondered why starting a
motor like a hair dryer or the motor on an air
conditioning system will initially dim the
lights in a house, but then the lights return to
normal? When the motor is turned on the full
120 V produces a very high current through
the resistance. This draws a great deal of
power which dims the lights. But after the
motor starts spinning, the back emf
decreases the net emf, the current drops
and the power usage of the motor
decreases, and the lights return to their
original level.
The structure of
DC motors and
DC generators is basically
the same, so a
DC generator can act as a
DC motor and a DC motor
can act as a DC generator.
Example 8: The armature
windings of a DC motor have a
resistance of 6 Ω. The motor is
powered with 120 V and
reaches its full speed against its
normal load. The back (counter)
emf is 106 V. Calculate the
current into the motor at full
speed.
A current-carrying coil of wire wrapped
around a metal loop produces a
magnetic field in the loop. If another
coil is wrapped around the other side of
the loop it will have an induced emf
produced if the field is changing.
If the number of loops in each coil is
different, the emf is proportionately
different in each of the coils. This called
a transformer.
There are two
types of
transformers:
Not really, the two types
are step-up and stepdown transformers.
Step-up transformers
increase the voltage,
step-down transformers
decrease the voltage.
The original coil of wire in a
transformer is the coil that
comes from the source and is
called the primary coil. The coil
where the induced emf is
produced is called the
secondary coil.
In a step-up transformer
the primary coil has less
loops than the secondary
coil. In a step-down
transformer the primary
coil has more loops than
the secondary coil.
The number of loops in
the coil is directly related
to the voltages: VS/VP =
NS/NP. Doubling the
number of loops in the
secondary coil doubles
the output voltage.
The power levels must
remain the same and
P = IV, so current must
change inversely with
voltage.
VS/VP = NS/NP = IP/IS
Example 9: The number of loops in
the primary coil of a transformer is
1200. The secondary coil has
120 loops. If the source voltage is
120 V, (a) what is the resulting
voltage? (b) What is the resulting
current if the initial current is 0.1 A?
(c) What type of transformer is
this?