Transcript Chapter 21 Magnetic Flux and Faraday`s Law of

Chapter 21
Magnetic Flux and Faraday’s
Law of Induction
What is E/M Induction?
Electromagnetic Induction is the process of
using magnetic fields to produce voltage,
and in a complete circuit, a current.
Michael Faraday first discovered it, using some of
the works of Hans Christian Oersted. His work
started at first using different combinations of wires
and magnetic strengths and currents, but it wasn't
until he tried moving the wires that he got any
success.
It turns out that electromagnetic induction is created
by just that - the moving of a conductive substance
through a magnetic field.
The Space Tether Experiment
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The Space Tether Experiment
•
The space tether experiment, a joint venture of the US and Italy, called for a scientific payload--a large, spherical
satellite--to be deployed from the US space shuttle at the end of a conducting cable (tether) 20 km (12.5 miles)
long. The idea was to let the shuttle drag the tether across the Earth's magnetic field, producing one part of a
dynamo circuit. The return current, from the shuttle to the payload, would flow in the Earth's ionosphere, which
also conducted electricity, even though not as well as the wire.
•
One purpose of such a set-up might be to produce electric power, generating current to run equipment
aboard the space shuttle. That electric comes at a price: it is taken away from the motion energy ("kinetic energy")
of the shuttle, since the magnetic force on the tether opposes the motion and slows it down. In principle, it should
also be possible to reverse this process: a future space station could use solar cells to produce an electric current,
which would be pumped into the tether in the opposite direction, so that the magnetic force would boost the orbital
motion and would raise the orbit to a higher altitude.
Magnetic Induction
As the magnet moves back and forth a current is said to be
INDUCED in the wire.
Faraday’s experiment: closing the switch in the
primary circuit induces a current in the
secondary circuit, but only while the current in
the primary circuit is changing.
• The current in the secondary circuit is zero as
long as the current in the primary circuit, and
therefore the magnetic field in the iron bar, is not
changing.
• Current flows in the secondary circuit while the
current in the primary is changing. It flows in
opposite directions depending on whether the
magnetic field is increasing or decreasing.
• The magnitude of the induced current is
proportional to the rate at which the magnetic
field is changing.
Note the motion of the magnet in each image:
Magnetic Flux
The first step to understanding the complex nature of
electromagnetic induction is to understand the idea of
magnetic flux.
Flux is a general term
associated with a FIELD that is
bound by a certain AREA. So
MAGNETIC FLUX is any AREA
that has a MAGNETIC FIELD
passing through it.
B
A
We generally define an AREA vector as one that is
perpendicular to the surface of the material.
Therefore, you can see in the figure that the AREA
vector and the Magnetic Field vector are PARALLEL.
This then produces a DOT PRODUCT between the 2
variables that then define flux.
Magnetic Flux
B  B  A
 B  BA cos 
2
Unit : Tm or Weber(Wb)
How could we CHANGE the flux over a period of
time?
 We could move the magnet away or towards (or
the wire).
 We could increase or decrease the area.
 We could ROTATE the wire along an axis that is
PERPENDICULAR to the field thus changing the
angle between the area and magnetic field vectors.
Magnetic flux is used
in the calculation of the
induced emf.
Faraday’s Law
Faraday learned that if you change any part of the flux over time
you could induce a current in a conductor and thus create a
source of EMF (electromotive force, voltage, potential difference). Since
we are dealing with time here, we are a talking about the RATE
of CHANGE of FLUX, which is called Faraday’s Law.
 B
 ( BA cos  )
  N
 N
t
t
N  # turns of wire
Faraday’s law: An emf is induced only when the
magnetic flux through a loop changes with time.
There are many devices that operate on the
basis of Faraday’s law.
An electric guitar
pickup:
The Forever Flashlight uses the Faraday Principle of
Electromagnetic Energy to eliminate the need for
batteries. The Faraday Principle states that if an
electric conductor, like copper wire, is moved through
a magnetic field, electric current will be generated and
flow into the conductor.
Tape recorder:
AC motors use Faraday’s law to
produce rotation and thus
convert electrical and
magnetic energy into
rotational kinetic energy. This
idea can be used to run all
kinds of motors. Since the
current in the coil is AC, it is
turning on and off thus
creating a CHANGING
magnetic field of its own. Its
own magnetic field interferes
with the shown magnetic field
to produce rotation.
DC motors use a commutator to change the direction of the current flow. This
keeps torque applied in one rotational direction.
Commutator
Transformers
Probably one of the greatest inventions of all time is the
transformer. AC Current from the primary coil moves
quickly BACK and FORTH (thus the idea of changing!)
across the secondary coil. The moving magnetic field
caused by the changing field (flux) induces a current in
the secondary coil.
If the secondary coil has MORE
turns than the primary you can
step up the voltage and runs
devices that would normally
need MORE voltage than what
you have coming in. We call this
a STEP UP transformer.
We can use this idea in reverse
as well to create a STEP DOWN
transformer.
Microphones
A microphone works when
sound waves enter the filter of
a microphone. Inside the filter,
a diaphragm is vibrated by the
sound waves which in turn
moves a coil of wire wrapped
around a magnet. The
movement of the wire in the
magnetic field induces a
current in the wire. Thus sound
waves can be turned into
electronic signals and then
amplified through a speaker.
Sample Problem: A coil of radius 0.5 m consisting
of 1000 loops is placed in a 500 mT magnetic
field such that the flux is maximum. The field
then drops to zero in 10 ms. What is the
induced potential in the coil?
Sample Problem: A coil of radius 0.5 m consisting
of 1000 loops is placed in a 500 mT magnetic
field such that the flux is maximum. The field
then drops to zero in 10 ms. What is the
induced potential in the coil?
Sample Problem: A coil with 200 turns of wire is wrapped on an
18.0 cm square frame. Each turn has the same area, equal to
that of the frame, and the total resistance of the coil is 2.0W . A
uniform magnetic field is applied perpendicularly to the plane of
the coil. If the field changes uniformly from 0 to 0.500 T in 0.80
s, find the magnitude of the induced emf in the coil while the
field has changed as well as the magnitude of the induced
current.
Sample Problem: A coil with 200 turns of wire is wrapped on an
18.0 cm square frame. Each turn has the same area, equal to
that of the frame, and the total resistance of the coil is 2.0W . A
uniform magnetic field is applied perpendicularly to the plane of
the coil. If the field changes uniformly from 0 to 0.500 T in 0.80
s, find the magnitude of the induced emf in the coil while the
field has changed as well as the magnitude of the induced
current.
Lenz’s Law
An induced current always flows in a direction
that opposes the change that caused it.
Therefore, if the magnetic field is increasing, the
magnetic field created by the induced current will
be in the opposite direction; if decreasing, it will
be in the same direction.
23-4 Lenz’s Law
This conducting rod
completes the circuit.
As it falls, the magnetic
flux decreases, and a
current is induced.
23-4 Lenz’s Law
The force due to the
induced current is
upward, slowing the fall.
23-4 Lenz’s Law
Currents can also flow in
bulk conductors. These
induced currents, called eddy
currents, can be powerful
brakes.
Lenz’s Law
Lenz's law gives the direction of the induced emf and current
resulting from electromagnetic induction. The law provides
a physical interpretation of the choice of sign in Faraday's
law of induction, indicating that the induced emf and the
change in flux have opposite signs.
Lenz’s Law
 B
  N
t
In the figure above, we see that the direction of the
current changes. Lenz’s Law helps us determine the
DIRECTION of that current.
Lenz’s Law & Faraday’s Law
 B
  N
t
Let’s consider a magnet with it’s north pole
moving TOWARDS a conducting loop.
DOES THE FLUX CHANGE?
Yes!
DOES THE FLUX INCREASE OR DECREASE?
Increase
WHAT SIGN DOES THE “” GIVE YOU IN
FARADAY’S LAW? Positive
B
induced
DOES LENZ’S LAW CANCEL OUT?
What does this mean?
NO
This means that the INDUCED MAGNETIC FIELD around the
WIRE caused by the moving magnet OPPOSES the original
magnetic field. Since the original B field is downward, the
induced field is upward! We then use the right hand rule to
determine the direction of the current.
Lenz’s Law
A magnet is
dropped down
a conducting
tube.
The INDUCED current creates an INDUCED
magnetic field of its own inside the conductor
that opposes the original magnetic field.
The magnet INDUCES a
current above and below
the magnet as it moves.
Since the
induced field
opposes the
direction of the
original it
attracts the
magnet upward
slowing the
motion caused
by gravity
downward.
Lenz’s Law
 B
  N
t
Let’s consider a magnet with it’s north pole
moving AWAY from a conducting loop.
DOES THE FLUX CHANGE?
Yes!
DOES THE FLUX INCREASE OR DECREASE?
Decreases
WHAT SIGN DOES THE “” GIVE YOU IN
FARADAY’S LAW?
negative
DOES LENZ’S LAW CANCEL OUT?
yes
B
What does this mean?
In this case, the induced field DOES NOT oppose the
original and points in the same direction. Once again
use your curled right hand rule to determine the
DIRECTION of the current.
induced
23-5 Mechanical Work and Electrical
Energy
This diagram shows the variables we need to
calculate the induced emf.
23-5 Mechanical Work and Electrical
Energy
Change in flux:
Induced emf:
Electric field caused by the motion of the
rod:
23-5 Mechanical Work and Electrical
Energy
If the rod is to move at a constant speed, an
external force must be exerted on it. This force
should have equal magnitude and opposite
direction to the magnetic force:
23-5 Mechanical Work and Electrical
Energy
The mechanical power delivered by the
external force is:
Compare this to the electrical power in the
light bulb:
Therefore, mechanical power has been
converted directly into electrical power.
Summary of Chapter 23
• A changing magnetic field can induce a current
in a circuit. The magnitude of the induced
current depends on the rate of change of the
magnetic field.
• Magnetic flux:
• Faraday’s law gives the induced emf:
Summary of Chapter 23
• Lenz’s law: an induced current flows in the
direction that opposes the change that created
the current.
• Motional emf:
• emf produced by a generator:
• An electric motor is basically a generator
operated in reverse.
• Inductance occurs when a coil with a changing
current induces an emf in itself.
Summary of Chapter 23
• Definition of inductance:
• Inductance of a solenoid:
• An RL circuit has a characteristic time
constant:
Summary of Chapter 23
• Current in an RL circuit after closing the switch:
• Magnetic energy density:
• Transformer equation: