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QUESTIONS? PLEASE ASK!
From last time…

Magnetic Flux
ΦB = BA = B A cos θ

Faraday’s Law: instantaneous emf
induced in a circuit = time rate of
change of magnetic flux through the
circuit
e = -N


DF B
Dt
Lenz’s Law:induced emf travels in
the direction that creates a
magnetic field with flux opposing
the change in the original flux
through the circuit
Motional emf: ε= B ℓ v
Motional EMF in a Circuit

Now place the conductor on
a pair of rails and pull it
with an applied force Fapp


assume the moving bar
has negligible resistance
The magnetic force Fapp on
the charges sets up an
induced current

the charges are free to
move in the closed path!
Motional emf in a Circuit II


The changing magnetic
flux through the loop
and the corresponding
induced emf in the bar
result from the change
in area of the loop
The induced ‘motional’
EMF acts like a battery
in the circuit
B v
e = B v and I =
R
20.4 Lenz’ Law Revisited


Current due to the induced EMF travels in
the direction that creates a magnetic field
with flux opposing the change in the
original flux through the circuit
In the diagram to the right, B is
decreasing with time



fB is decreasing; current I is induced in
counterclockwise direction to increase fB
If B were increasing with time, then the
induced current would travel in the
clockwise direction
When applying Lenz’ Law, there are two
magnetic fields to consider


The external changing magnetic field that
induces the current in the loop
The magnetic field produced by the current
in the loop
Lenz’ Law Revisited,
Conservation of Energy
Assume the induced current
I is clockwise in the figure

The magnetic force Fm on
the bar would be to the right
Fm causes bar to accelerate
v would increase



Magnetic flux fB would
increase
Current I would increase in
clockwise direction



A perpetual motion
machine?? Sorry…


Violation of conservation of
energy is not allowed!!
Thus, current I is
counterclockwise
Example Problem 20.32
A conducting bar of length L = 35
cm moves to the right on two
frictionless rails connected by a
resistor R = 9.0 Ω. A uniform
magnetic field directed into the page
has a magnitude of 0.30 T.
(a) At what speed should bar move
to produce an 8.5 mA current in the
resistor?
(b) At what rate is energy delivered
to the resistor?
(c) Explain the origin of energy
being delivered to the resistor.
20.5 Generators

Alternating Current (AC) generator

Converts mechanical energy to
electrical energy using induction




The opposite of a motor!
Consists of a wire loop rotated by
some external means
falling water (hydroelectric), heat
by burning coal to produce steam
(coal-fired), nuclear fission reactor,
solar heater
Basic AC generator operation


Loop rotates from external force,
Magnetic flux through the loop
changes with time, inducing an EMF
and a current in the external circuit


The ends of the loop are connected
to slip rings that rotate with the loop
Connections to the external circuit
are made by stationary brushes in
contact with the slip rings
AC Generators, mathematics

The emf generated by
the rotating loop can be
found by:
ε =2 B ℓ v=2 B ℓ v sin θ

If the loop rotates with a
constant angular speed,
ω, and N turns:
 θ = ω t
 v = r ω = (a/2) ω

A=ℓa
ε = N B A ω sin ω t
a/2
Example Problem 20.37
In a model AC generator, a 500 turn
rectangular coil 8.0 cm by 20 cm rotates
at 120 rev/min in a uniform magnetic field
of 0.60 T
(a) What is the maximum EMF induced in
the coil?
(b) What is the instantaneous value of
EMF in the coil at t = (p/32) s? Assume
the EMF is zero at t = 0
(c)What is the smallest value of t for
which the EMF will have its maximum
value?
Motors and Back EMF

Motors convert electrical
energy into mechanical energy



A motor is a generator run in
reverse
Back EMF is the self-induced
EMF that tends to reduce the
applied current
When a motor is turned on, no
back EMF initially

The current is very large
because it is limited only by
the resistance of the coil
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Motors and Back EMF



As the coil begins to
rotate, the induced back
emf opposes the applied
voltage
The current in the coil is
reduced
The power requirements
for starting a motor and
for running it under heavy
loads are greater than
those for running the
motor under average
loads
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20.6 Self-inductance


Self-inductance occurs when
the changing flux through a
circuit arises from the circuit
itself
The self-induced EMF must
be proportional to the time
rate of change of the current
e = -L


DI
Dt
L is inductance of the
device
The negative sign is
important! It indicates that a
changing current induces an
EMF in opposition to that
change
Self-inductance


The inductance of a coil depends
on geometric factors
The SI unit of self-inductance is
the Henry


1 H = 1 (V · s) / A
The expression for L is
L=N
DFB
DI
=
N FB
I
Solution to 20.32
Solution to 20.37