```Chapter 31: Faraday’s Law
Chapter Outline
• Induced EMF
• Lenz’s Law
• EMF Induced in a Moving Conductor
• Electric Generators
• Back EMF & Counter Torque
• Eddy Currents
• Transformers & Transmission of Power
A Changing Magnetic Flux
Produces an Electric Field
• Applications of Induction:
Sound Systems, Computer Memory, Seismograph,….
1791 – 1867
• British physicist & chemist
• Great experimental scientist
Contributions to Electricity:
1. Electromagnetic induction
2. Laws of electrolysis
Inventions
1. Motor
2. Generator
3. Transformer
1. Whenever the magnetic field about an
electromagnet was made to grow &
collapse by closing & opening the
electric circuit of which it was a part,
An electric current could be
detected in a separate
conductor nearby.
2. Moving a permanent magnet into &
out of a coil of wire
Also induced a current in the wire
while the magnet was in motion.
3. Moving a conductor near a stationary permanent magnet
caused a current to flow in the wire also,
as long as it was moving.
Induced EMF
• Michael Faraday looked for evidence
that a magnetic field would induce an
electric current with this apparatus:
• He found no evidence when the current was steady. He saw
an induced current when the switch was turned on or off.
He concluded:
A Changing Magnetic Field Induces an EMF.
• His experiment used a magnetic field that was changing because
the current producing it was changing; the picture shows a
magnetic field that changes because the magnet is moving.
EMF Produced by a Changing
Magnetic Field
• A loop of wire is connected
to a sensitive ammeter.
• When a magnet is moved
toward the loop, the
ammeter deflects.
– The direction was arbitrarily
chosen to be negative.
• When the magnet is held
stationary, there is no
deflection of the ammeter.
• Therefore, there is no
induced current.
– Even though the magnet is
in the loop
•If the magnet is moved
away from the loop.
•The ammeter deflects
in the opposite
direction!
Induced Current, Summary
• A primary coil is connected
to a switch and a battery.
• The wire is wrapped around
an iron ring.
• A secondary coil is also
wrapped around the iron ring.
No battery is present in
the secondary coil.
• The secondary coil is not directly
connected to the primary coil.
Close the switch
& observe the
on the ammeter.
• At the instant the switch is closed,
the ammeter changes from zero in one
direction, then returns to zero.
• When the switch is opened,
the ammeter changes in the opposite
direction, then returns to zero.
• The ammeter reads zero when there is a
steady current or when there is no
current in the primary circuit.
• An electric current can be induced in a loop
by a changing magnetic field.
–This would be the current in the secondary
circuit of this experimental set-up.
• The induced current exists only while the
magnetic field through the loop is changing.
• This is generally expressed as:
An induced emf is produced in the loop
by the changing magnetic field.
• Just the existence of the magnetic flux is not sufficient to
produce the induced emf, the flux must be changing.
Faraday’s Law of Induction: Lenz’s Law
• Faraday found that the induced emf in a wire loop is
Proportional to the time Rate of Change of the
Magnetic Flux Through the Loop.
• Magnetic Flux is defined similarly to electric flux:

• If B is constant over the surface area A, then
ΦB = BA = BA cosθ
(The scalar or dot product of vectors B & A)
• The SI Unit of Magnetic flux = Weber (Wb):
1 Wb = 1 T·m2.
This figure shows the variables in the flux equation:
ΦB = BA = BA cosθ
• Magnetic Flux is analogous to electric flux: It
is proportional to the total number of
magnetic field lines passing through the loop.
Conceptual Example: Determining Flux
• A square loop of wire encloses area A1. A uniform
magnetic field B perpendicular to the loop extends
over the area A2.
• What is the magnetic flux through the loop A1?
“The emf induced in a circuit is equal
to the time rate of change of magnetic
flux through the circuit.”
For a coil of N turns:
• The minus sign gives the direction of
the induced emf.
 Lenz’s Law:
A current produced by an
induced emf moves in a direction
so that the magnetic field
IT PRODUCES
tends to restore the changed field.
• The minus sign gives the direction of
the induced emf.
 Lenz’s Law:
Alternative Statement:
An induced emf is always
in a direction that OPPOSES
the original change in flux
that caused it.
Example
• Assume a loop enclosing
an area A lies in a
uniform magnetic field.
• The magnetic flux
through the loop is
ΦB = BA = BAcos(θ)
•The induced emf is
 = - (d[BAcos(θ)]/dt)
Methods of Inducing an EMF
• The magnitude of the magnetic field can
change with time.
• The area enclosed by the loop can
change with time.
• The angle between the magnetic field
& the normal to the loop can change
with time.
• Any combination of the above can occur.
Example
A Loop of Wire in a Magnetic Field
• A square loop of wire of side l = 5.0 cm is in a
uniform magnetic field B = 0.16 T.
Calculate
(a) The magnetic flux in the loop when B is
perpendicular to the face of the loop.
(b) The magnetic flux in the loop when B is at an
angle of 30° to the area A of the loop,
(c) The magnitude of the average current in the loop
if it has a resistance of R = 0.012 Ω and it is
rotated from position (b) to position (a) in 0.14 s.
The Magnetic Flux will change
if the area of the loop changes.
Magnetic Flux will change if the angle
between the loop & the field changes.
Conceptual Example: Induction stove.
In an induction stove, an ac current exists in a coil
that is the “burner” (a burner that never gets hot). Why
will it heat a metal pan but not a glass container?
Problem Solving: Lenz’s Law
1. Determine whether the magnetic flux is
increasing, decreasing, or unchanged.
2. The magnetic field due to the induced current
points in the opposite direction to the original
field if the flux is increasing; in the same
direction if it is decreasing; and is zero if the flux
is not changing.
3. Use the right-hand rule to determine the
direction of the current.
4. Remember that the external field and the field
due to the induced current are different.
Conceptual Example: Practice with Lenz’s Law
In which direction is the current induced in the circular
loop for each situation?
Example
Pulling a coil from a magnetic field.
• A 100-loop square coil of wire, with
side l = 5.00 cm & total resistance
100 Ω, is positioned perpendicular to
a uniform 0.600-T magnetic field. It
is quickly pulled from the field at
constant speed (moving perpendicular to
B) to a region where B drops to zero.
• At t = 0, the right edge of the coil is at the edge of the field. It
takes 0.100 s for the whole coil to reach the field-free region.
Find: (a) the rate of change in flux through the coil, and
(b) the emf and current induced.
(c) the energy dissipated in the coil.
(d) the average force required (Fext).