Faraday’s Law of Induction

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Faradays Law of Induction

• AP Physics C
• Montwood High School
• R. Casao

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• Two simple experiments demonstrate that a current
  can be produced by a changing magnetic field.
• First consider a loop of wire connected to a
  galvanometer as shown.

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• If a magnet is moved toward the loop, the
  galvanometer needle will deflect in one
  direction.

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• If a magnet is moved away from the loop, the
  galvanometer needle will deflect in the opposite
  direction.

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• If the magnet is held stationary relative to the
  loop, no galvanometer needle deflection is
  observed.

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• If the magnet is held stationary and the coil is
  moved toward or away from the magnet, the
  galvanometer needle will also deflect.
• From these observations, you can conclude that a
  current is set up in the circuit as long as there
  is relative motion between the magnet and the
  coil.
• This current is set up in the circuit even though
  there are no batteries in the circuit.
• The current is said to be an induced current,
  which is produced by an induced EMF.

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Faradays Experiment

• A coil is connected to a switch and a battery.
• This is called the primary coil and the circuit
  is called the primary circuit.
• The coil is wrapped around an iron ring to
  intensify the magnetic field produced by the
  current through the coil.

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Faradays Experiment

• A second coil, on the right, is wrapped around
  the iron ring and is connected to a galvanometer.
• This is secondary coil and the circuit is the
  secondary circuit.
• There is no battery in the secondary circuit and
  the secondary circuit is not connected to the
  primary coil.

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Faradays Experiment

• The only purpose of this circuit is to detect any
  current that might be produced by a change in the
  magnetic field.
• When the switch in the primary circuit is closed,
  the galvanometer in the secondary circuit
  deflects in one direction and then returns to
  zero.

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Faradays Experiment

• When the switch is opened, the galvanometer
  deflects in the opposite direction and again
  returns to zero.
• The galvanometer reads zero when there is a
  steady current in the primary circuit.

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• Faraday concluded that an electric current can be
  produced by a changing magnetic field.
• A current cannot be produced by a steady magnetic
  field.
• The current that is produced in the secondary
  circuit occurs for only an instant while the
  magnetic field through the secondary coil is
  changing.
• In effect, the secondary circuit behaves as
  though there were a source of EMF connected to it
  for a short instant.
• An induced EMF is produced in the secondary
  circuit by the changing magnetic field.

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• In both experiments, an EMF is induced in a
  circuit when the magnetic flux through the
  circuit changes with time.
• Faradays Law of Induction The EMF induced in a
  circuit is directly proportional to the time rate
  of change of magnetic flux through the circuit.
• where Fm is the magnetic flux threading the
  circuit.
• Magnetic flux Fm

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• The integral of the magnetic flux is taken over
  the area bounded by the circuit.
• The negative sign is a consequence of Lenzs law
  and is discussed later (the induced EMF opposes
  the change in the magnetic flux in the circuit).
• If the circuit is a coil consisting of N loops
  all of the same area and if the flux threads all
  loops, the induced EMF is

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• Suppose the magnetic field is uniform over a loop
  of area A lying in a plane as shown in the figure
  below.
• The flux through the loop is equal to BAcos ?
  and the induced EMF is

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• An EMF can be induced in the circuit in several
  ways
• The magnitude of B can vary with time
• The area of the circuit can change with time
• The angle ? between B and the normal to the plane
  can change with time and
• Any combination of these can occur.

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Application of Faradays Law

• A coil is wrapped with 200 turns of wire on the
  perimeter of a square frame of sides 18 cm. Each
  turn has the same area, equal to that of the
  frame, and the total resistance of the coil is 2
  ?. A uniform magnetic field is turned on
  perpendicular to the plane of the coil. If the
  field changes linearly from 0 to 0.5 Wb/m2 in a
  time of 0.8 s, find the magnitude of the induced
  EMF in the coil while the field is changing.
• Loop area (0.18 m)2 0.0324 m2
• At t 0 s, the magnetic flux through the loop is
  0 since B 0 T.

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Application of Faradays Law

• At t 8 s, the magnetic flux through the loop is
  Fm BA 0.5 Wb/m20.0324 m2 0.0162
  Wb.
• The magnitude of the induced EMF is

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Exponentially Decaying B Field

• A plane loop of wire of area A is placed in a
  region where the magnetic field is perpendicular
  to the plane. The magnitude of B varies in time
  according to the expression B Boe-at. That
  is, at t 0 s, the field is Bo, and for t gt 0,
  the field decreases exponentially in time. Find
  the induced EMF in the loop as a function of
  time.
• At t 0 s, B is perpendicular to the plane of
  the loop and is a maximum.
• The magnetic flux through the loop at time t gt 0
  is

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Applications of Faradays Law

• The ground fault interrupter (GFI) is a safety
  device that protects users of electrical
  appliances against electric shock by making use
  of Faradays law.
• Wire 1 leads from the
• wall outlet to the
• appliance to be
• protected.
• Wire 2 leads from the
• appliance back to
• the wall outlet.

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• An iron ring surrounds the two wires, and a
  sensing coil is wrapped around part of the ring.
• Because the currents in the wires are in opposite
  directions, the net magnetic flux through the
  sensing coil due to the currents is zero.
• If the return current in wire 2 changes, the net
• magnetic flux thru
• the sensing coil is no
• longer zero.
• This can happen if the
• appliance becomes wet,
• enabling the current to leak
• to the ground.

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• Because household current is alternating (its
  direction keeps reversing), the magnetic flux
  through the sensing coil changes with time,
  inducing an EMF if the coil.
• The induced EMF is used to trigger a circuit
  breaker, which stops the current before it is
  able to reach a harmful level.
• Electric Guitar
• The coil is called a pickup coil and is placed
  near the vibrating guitar string, which is made
  of a metal that can be magnetized.
• A permanent magnet inside the coil temporarily
  magnetizes the portion of string nearest the coil.

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• When the string vibrates at some frequency, its
  magnetized section produces a changing magnetic
  flux thru the coil.

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• The changing flux induces an EMF in the pickup
  coil that is fed to an amplifier.
• The output of the amplifier is sent to the
  speakers, which produce the sound we hear.

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A Note on the Magnitude of an Induced Current

• The induced current in the conducting loop has
  the same magnitude at all points in the loop.