Chapter 29 Electromagnetic Induction

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Chapter 29 Electromagnetic Induction

• Consider Faradays Law
• Consider Lenzs Law
• Study motional emf
• Explore induced electric fields
• Eddy currents
• Displacement current
• Introduction to Maxwells equations
• Superconductivity and Magnetism

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Induced EMF Experiments
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Faradays Law of Induction

• The induced emf is proportional to the rate of
  change of magnetic flux , ,through the
  coil.
• B, the magnetic field can change with time.
• A, the area can change with time

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Faradays Law Area and Magnetic Flux Direction

• Regardless of what moves, knowing the magnetic
  flux around a conducting entity will allow
  determination of current induced.

For a uniform B field
Faradays Law of Induction
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Electromagnetic Induction (Chapter 29, Sec 2)
Example 29-1 EMF and Current Induced in a Loop
A 120 cm2
R (loop resistance) 5 ?
Determine induced voltage (VEMF Vab). Determine
induced current (I). Verify current direction
using Lenzs Law.
Figure 29-4
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• Lenzs Law
• The direction of any magnetic induction effect is
  such as to oppose the cause of the effect.
• The cause can be a change flux, or the motion
  of a conductor.
• In all cases the induced current tries to prevent
  the status quo by opposing motion or change of
  flux.

• The induced current due to the change in B is
  clockwise as seen from above the loop. (RHR
  opposite direction of fingers)
• The Binduced that it caused is downward, opposite
  the change in the upward field B.

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Lenzs Law I Counter clockwise induced current
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Lenzs Law II clockwise induced current
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A Simple Alternator (generator)
? ?t, where ? is the angular velocity of the
loop.
(?B is the total magnetic flux penetrating area A
)
For an N-turn coil,
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DC generator and the average back emf

• The back emf in a motor is the absolute value of
  the alternator emf.

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Motional Electromotive Force

• As the rod moves the magnetic field causes
  positive free charge to go to move to one end and
  negative charge to the other.
• Equilibrium is established when the magnetic
  force equals the electric force.

B
E
At equilibrium
for ? 90
(29.6)
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A conducting rod moving in a uniform magnetic
field
dA
Figure 29-10
Faradays Law of Induction The induced emf (?) in
a closed loop equals the negative of the time
rate of change of magnetic flux through the loop.
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Changing the Coil Shape
Change the shape of the coil and you change the
shape of the magnetic flux. The rate at which you
change the shape is the rate of change of the
magnetic flux This induces a current in the coil
to oppose the change in flux.
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Changing Magnetic fields will Induced electric
fields

• The windings of a long solenoid carrying a
  current I

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Eddy currents

• Induced currents produce eddy currents that
  oppose the induced currents (and the motion of
  the disk)

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Displacement current and Maxwells equations

• A varying electric field will give rise to a
  magnetic field.
• Explains electromagnetic waves.

Displacement current iD between plates
Proof of iD is the measure magnetic field between
plates
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Superconductivity and the Meissner effect

• When cooled below the critical temperature,
  superconductive materials lose all resistance to
  electrical current.
• Refer to Figures 29.24 and 29.25 at right.

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