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Electromagnetic
Induction
Unit 6
Where We Are
• We will be covering four lessons in this
unit.
• This material will not be on Friday’s
test.
• However, there will be a ~20-30 min
quiz on this material next Wednesday.
Where We Are
• In the last unit, we saw two ways in
which electricity and magnetism are
related:
– Electric currents produce magnetic fields.
– Magnetic fields exert forces on electric
currents.
• Scientists began to wonder if magnetic
fields could produce electric currents.
Faraday and Induced EMFs
• Michael Faraday conducted a series of
experiments to see if he could use a
magnet to produce a current.
• A coil of wire was connected to a
battery.
Faraday and Induced EMFs
• The current through coil x produced a
magnetic field, which was amplified by the
iron core.
• A second coil, Y, was hooked up to a
galvanometer, which would detect even a
small current, but not to a battery.
Faraday and Induced EMFs
• Faraday hoped that a strong, steady
current through coil X would produce a
current in coil Y.
• However, no current was observed,
even when a very strong current was
used.
Faraday and Induced EMFs
• However, Faraday noticed that the
galvanometer jumped when at the moment
he closed the switch in circuit X.
• The needle jumped in the opposite direction
at the moment opened the switch.
Faraday and Induced EMFs
• A constant current in X produced no
current in Y.
• Only when the current in X was starting
or stopping was a current observed in
Y.
Faraday and Induced EMFs
• As the current is turning on or off, the
magnetic field generated by X is
changing.
• When the B field was changing, an
induced current was observed in Y
Faraday and Induced EMFs
• Since current arises when there is an
EMF (like a battery) in the circuit,
Faraday concluded:
A changing magnetic field
induces an EMF.
• WARNING: Steady B fields do nothing.
Only changing B fields produce EMFs.
Faraday and Induced EMFs
• This phenomenon is called
electromagnetic induction.
• Faraday went on to do further
experiments with this phenomenon.
Faraday and Induced EMFs
• Faraday showed that if a magnet is
moved quickly into a coil of wire, a
current is induced.
• If the magnet is removed, a current is
induced in the opposite direction.
Faraday and Induced EMFs
• Faraday also showed that the same effect
occurs if the magnet is held steady and the
coil of wire is moved.
• Motion or change is required to induce an
EMF, but it is only relative motion that
counts.
COOL VIDEO
Magnetic Flux
• As Faraday began quantitative
investigations of these effects, he
discovered the strength of the EMF did
not just depend on how fast B was
changing.
• It also depended on the area enclosed
by the loop of wire, and the angle
between the wire and the B field.
Magnetic Flux
• These effects are unified
in the concept of
magnetic flux.
• Magnetic flux is a
measure of the number
of magnetic field lines
that pass through a
surface with a given
area.
Magnetic Flux
• Magnetic flux is denoted
B, and is calculated
using the formula
FB = BAcosq
Magnitude of
the B field
Angle between
B a line
Area of the perpendicular
surface
to A
Magnetic Flux
• These effects are unified
in the concept of
magnetic flux.
• Magnetic flux is a
measure of the number
of magnetic field lines
that pass through a
surface with a given
area.
Magnetic Flux
• Notice that the magnetic flux is greatest
when the magnetic field is perpendicular to
the surface.
• Magnetic flux is measured in webers.
1Wb =1 T× m
2
Conceptual Example:
Magnetic Flux
A square loop of wire encloses an area A1 as shown. Inside
the wire is a region of uniform magnetic field, B, perpendicular
to the loop. The B field extends over area A2. What is the
magnetic flux through the loop of wire?
Example: Magnetic Flux
A square loop of wire is in a 1.25 T magnetic field. If the length
of each side of the loop is 10 cm,
a) What are the maximum and minimum values for the
magnetic flux through the loop?
b) What is the flux when the angle between B and the
line perpendicular to A is 35º?
Homework
• Read sections 21-1 and 21-2.
• Do problem 7 on page 610.
Faraday’s Law of Induction
Faraday’s Law of Induction
• Faraday determined the induced EMF
depended on a change in the B field.
• It also depended on the area of the loop
of wire, and the angle the loop was
placed at.
• All of these items are represented in the
concept of magnetic flux developed
yesterday.
Faraday’s Law of Induction
• Faraday concluded at a change in
magnetic flux over a time interval t will
induce an EMF in a loop of wire.
• Mathematically, this is represented by
• We will talk about the minus sign in a
moment.
Faraday’s Law of Induction
• If the wire has multiple coils, the EMF is
multiplied by the number of coils. So
• Here, N is the number of coils in the wire
loop.
• This is Faraday’s Law of Induction.
Example: Faraday’s Law
A square coil of wire (sides of length 5 cm) is initially in a
0.6 T magnetic field as shown. It is quickly pulled out of the
field to a region where B = 0. If it takes 0.1 s for the entire
coil to leave the field, what EMF is induced in the coil?
Lenz’s Law
Lenz’s Law
• You have already noticed the odd minus
sign in Faraday’s Law.
• You might also have noticed that we did
not specify a direction for the current in
the last example.
• Both of these are explained by Lenz’s
Law.
Lenz’s Law
• Lenz’s Law states
The current produced by an induced EMF
moves in a direction so that its magnetic
field opposes the original change in flux.
• Be careful here: we are now talking
about two separate magnetic fields.
– The magnetic field generating the change
in flux.
– The magnetic field produced by the
induced current.
Lenz’s Law
• Here’s a helpful way to think about Lenz’s
Law:
– When the flux through a loop changes, magnetic
field line are either being “lost” or “gained.”
– If flux goes down and lines are “lost” the current
moves to generate a B field to “replace” those lost
lines.
– If the flux goes up and lines are “gained” the
current moves to generate a B field pointing in the
opposite direction to “cancel out” those new lines.
Conceptual Example
Conceptual Example
Example: Faraday’s Law
Let’s revisit the last example:
a) What direction is the
current flowing?
b) How much current is flowing?
c) If the coil has a resistance of
100 , how much energy is
dissipated in the coil in the 0.1 s
of motion?
Homework
• Do problems 1, 2, and 7 on page 610.
Problem Day
• Do problems 4, 5, 9, and 10 on page
610.
Homework
• Read sections 21-3 and 21-4.
• Do problems 11 and 13 on page 611.
EMF in a Moving Conductor
EMF on a Moving Conductor
• Suppose we have the following setup:
• A conducting rod is moving with speed v
as shown.
EMF on a Moving Conductor
• Lenz’s Law tells us that this will create a
current that flows in a direction that opposes
the change in flux.
• We want to quantify the EMF through
Faraday’s Law.
EMF on a Moving Conductor
• As the rod moves, the size of the loop is
increased.
• This means the magnetic flux through
the loop is increasing.
EMF on a Moving Conductor
• Faraday’s Law tells us that the EMF is
found by
FB = BAcosq
EMF on a Moving Conductor
• So, the change in flux is
EMF on a Moving Conductor
• To find the change in area, notice that
the rod travels a distance
in the time t.
EMF on a Moving Conductor
• This means the change in area is
• And the change in flux is
EMF on a Moving Conductor
• Plugging this into Faraday’s Law
EMF on a Moving Conductor
• Plugging this into Faraday’s Law
e =B v
Example: Airplane
An airplane is traveling at 1000 km/hr. If the Earth’s magnetic
field is 5 x 10-5 T and points vertically. If the wingspan of the
plane is 70 m, what is the EMF induced in the wings of the
plane?