FARADAYS LAW

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FARADAYS LAW

• Michael Faraday and Joseph Henry discovered it in
  1831
• Changing magnetic flux produces an emf
• Or Changing B-Field produces E-Field
• The rate of change of magnetic flux is required

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Induced EMF produced by a changing Magnetic
Flux!
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Changing Flux due to moving permanent magnet
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Nature of a changing flux

• Since flux is defined as a dot product
• B can change
• A can change
• q can change

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Sample prob. 30-1Calculate induced emf in coil C
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LENZS Law (no such thing as a perpetual motion
machine
The direction of the emf induced by changing
flux will produce a current that generates a
magnetic field opposing the flux change that
produced it
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LENZS LAW

• The polarity of the emf induced by a changing
  flux will produce a current that generates a
  magnetic field opposing the flux change that
  produced it

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Sample prob. 30-2 Example what is the emf in
loop and what is the net current ?
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Sample 30-3 Find emf when B is not uniform
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Induced electric fields

• The electric field due to an emf is NOT
  conservative
• Net work must be done over a closed path
  (circuit)
• Therefore, the closed path integral of E is
  non-zero
• Charges will accelerate parallel to E.

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Induced electric fields

• The electric field due to an emf is NOT
  conservative
• Net work must be done over a closed path
  (circuit)
• Therefore, the closed path integral of E is
  non-zero
• Charges will accelerate parallel to E.

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Induced electric fields
We will assume here that B is increasing into
the page
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Sample problem
If R8.5 cm and
a) Find E when r5.2cm
b) Find E when r12.5 cm
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INDUCTANCEAn Application of Faradays Law

• Definition
• Units
• Self inductance
• Examples
• Mutual inductance
• Example
• Energy in Inductor
• LR circuit
• exponential growth and decay

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Definition and Units

• based on Faradays Law
• assume A and q are constant when determining flux
• B is proportional to i
• Unit is henry (H) equals volt-second/meter

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Inductors and self inductance Land Back
EMF-voltage
Changing flux induces emf in same element that
carries current A back emf is generated by a
changing current emf opposes the change causing
it (Lenzs Law) emf thus opposes the changing
current (i.e., back emf)
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Time dependence of an LR circuit
At t 0, i 0, and switch is just closed
Apply Kirchhoffs Loop Rule
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LR circuit - initial current is
Apply Kirchhoffs Loop Rule
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Motional emf
The current follows the prediction from Lenzs
Law The experiment that tells you there is no
perpetual motion machine. What is the power
consumed by the resistor in terms of B and v?
The wire has resistance so we can think of an
effective circuit
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Self inductance of a flat coil

• Determine the flux through the center of the coil

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Self inductance of a coaxial cable

• The flux is due to the field of the central
  wire passing through the blue area

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Mutual inductance

• A changing flux in one element induces an emf in
  another
• Multiple inductors can exhibit combined self and
  mutual inductance

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Energy in an inductor

• Start with the power delivered to the inductor

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Energy density in an inductor

• Determine the energy in a solenoid

Above is general result
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Motional emf
The velocity is not a constant (angular velocity
is) for the rod in this problem, how would you
solve it?
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Motional emf

• Apply the Lorentz Force Equation

Can you arrive at the same result starting with
Faradays Law?