Magnetic Flux and Faraday

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Chapter 23 Magnetic Flux and Faradays Law of
Induction
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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.
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Magnetic Induction

• As the magnet moves back and forth a current is
  said to be INDUCED in the wire.

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Faradays 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.
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• 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.

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Note the motion of the magnet in each image
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Magnetic Flux

• The first step to understanding the complex
  nature of electromagnetic induction is to
  understand the idea of magnetic flux.

B
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.
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.
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Magnetic Flux

• 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.

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Magnetic flux is used in the calculation of the
induced emf.
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Faradays 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
  (voltage, potential difference). Since we are
  dealing with time here were a talking about the
  RATE of CHANGE of FLUX, which is called Faradays
  Law.

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Faradays law An emf is induced only when the
magnetic flux through a loop changes with time.
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There are many devices that operate on the basis
of Faradays law.
An electric guitar pickup
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• 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.

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• AC Generators use Faradays 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.

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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.
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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.

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• 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?

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• 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?

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• 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.

4.05 V
2.03 A
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Lenzs 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.
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23-4 Lenzs Law
This conducting rod completes the circuit. As it
falls, the magnetic flux decreases, and a current
is induced.
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23-4 Lenzs Law
The force due to the induced current is upward,
slowing the fall.
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23-4 Lenzs Law
Currents can also flow in bulk conductors. These
induced currents, called eddy currents, can be
powerful brakes.
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Lenzs 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.

Lenzs Law
In the figure above, we see that the direction of
the current changes. Lenzs Law helps us
determine the DIRECTION of that current.
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Lenzs Law Faradays Law
Lets consider a magnet with its north pole
moving TOWARDS a conducting loop. DOES THE FLUX
CHANGE? DOES THE FLUX INCREASE OR
DECREASE? WHAT SIGN DOES THE D GIVE YOU IN
FARADAYS LAW? DOES LENZS LAW CANCEL OUT? What
does this mean?
Yes!
Increase
Positive
NO
Binduced
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.
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Lenzs Law
The INDUCED current creates an INDUCED magnetic
field of its own inside the conductor that
opposes the original magnetic field.
Since the induced field opposes the direction of
the original it attracts the magnet upward
slowing the motion caused by gravity downward.
A magnet is dropped down a conducting tube.
The magnet INDUCES a current above and below the
magnet as it moves.
If the motion of the magnet were NOT slowed this
would violate conservation of energy!
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Lenzs Law
Lets consider a magnet with its north pole
moving AWAY from a conducting loop. DOES THE
FLUX CHANGE? DOES THE FLUX INCREASE OR
DECREASE? WHAT SIGN DOES THE D GIVE YOU IN
FARADAYS LAW? DOES LENZS LAW CANCEL OUT? What
does this mean?
Yes!
Decreases
negative
yes
Binduced
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.
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23-5 Mechanical Work and Electrical Energy
This diagram shows the variables we need to
calculate the induced emf.
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23-5 Mechanical Work and Electrical Energy
Change in flux Induced emf
Electric field caused by the motion of the rod
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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
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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.
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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
• Faradays law gives the induced emf

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Summary of Chapter 23

• Lenzs 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.

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Summary of Chapter 23

• Definition of inductance

• Inductance of a solenoid

• An RL circuit has a characteristic time constant

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Summary of Chapter 23

• Current in an RL circuit after closing the
  switch

• Magnetic energy density

• Transformer equation