20 Overview

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20 Overview
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• current ? magnetic field
• magnetic field ? current
• Laws of Faraday Lenz
• transformers power transmission
• Homework
• 4, 9, 15, 19, 26, 45, 55, 69, 78.

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Motional EMF
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• magnetic force on free charges creates voltage
  across rod
• qE qvB
• E vB
• EL vBL
• emf vBL

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0
A (d 1m) bar moves (v 20 m/s) as shown. (B
0.25 T). Calculate the emf and the current in
the resistor (R 5.0 O).
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Magnetic Flux

• Motional emf works for straight wires, but not
  for loops
• Solution Magnetic Flux Concept
• Faradays Law Voltage induced in loop equals the
  _______ the Magnetic Flux
• ______________.
• Magnetic Flux is a field x area product
• Unit Tm2

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Magnetic Flux Concept

• Method Draw field lines loop
• Flux is the lines passing thru loop
• Draw the change
• Voltage rate of change in lines thru loop

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Calculating B-Flux
Ex. B 1.0T, Area 10. sq.m., angle 30
degrees.
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Faradays Law
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(1 Tm2 /s 1 volt)
N is number of turns of wire on loop. Ex. 50
turns of wire has
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What motions produce a change in flux thru the
single loop? If the single loop is moved to the
right, what is the direction of the current
induced in it?
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Which of the following can produce a changing
magnetic flux?

1. B change
2. Area change
3. angle change
4. none of these
5. all of these

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Lenzs Law
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• induced voltage opposes the change which produced
  it
• Ex A magnet moving in or out of a coil feels a
  magnetic force which opposes the motion of the
  magnet
• Ex. Lenz Law Tube

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0
Ex. A 1.0 sq.m. loop has 60 turns. Its normal is
parallel to a uniform B-field of strength 0.10 T.
It is rotated so its normal is perpendicular to B
in a time of 1.0s. Calculate the voltage induced.
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Applications of Faradays Law
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• Pick up coils
• Generators

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Alternating Current (AC) Generators
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• Coil rotates at ? ?/t (? ?t)
• Rotation ? flux change
• Voltage NBA?sin(?t)

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a) What must be the magnetic field strength so
that a generator consisting of 1000 turns of a
coil of radius 25 cm produces a peak output of
160 V when turned at a frequency of 60 Hz? b)
Sketch a graph of the output of the generator.
0
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Transformers

• Flux ?FB/?t _________ for each coil
• By Faradays Law
• Vp Np ?FB/?t and
• Vs Ns ?FB/?t

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Power and Current in Transformers

• Conservation of Energy implies power at primary
  is the same as power at secondary
• ______________
• Ex A transformer increases voltage by a factor
  of ten, the output (secondary) current decreases
  by a factor of ten

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Electromagnetic Waves

• Faraday time varying B produces time varying E
• Maxwell time varying E produces time varying B
• i.e. one begets the other self-sustaining,
  time-varying EM wave is produced

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Polarization

• overall orientation of electric field of light
• simplest cases unpolarized (radial), plane
  polarized (linear)

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Polarizing Filters

• Polarizing material allows the passage of only
  one direction of E
• Malus Law

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Properties of Electromagnetic Waves

• travel in vacuum
• transverse waves
• speed in a vacuum governed by magnetic and
  electric constants of free space
• c fl 299,792,458 m/s (3.00 x 108 m/s)

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Spectrum by Wavelength

• microwaves cm range waves strongly absorbed by
  water. cold spots separated by half-wavelength
• infrared (IR) mm to um waves also strongly
  absorbed by water
• radio waves wavelengths 1 to 500 meters
• Ex. f 100 MHz. What is its wavelength?
• visible 400 to 700 nm (400 is violet, 700 is
  red)
• ultraviolet (UV) 0.1 to 100 nm, causes sunburn
• x-ray 0.01 to 0.001 nm waves can pass through
  10cm of many materials
• gamma-rays lt 0.001 nm waves are even more
  penetrating

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Standing Waves

• Confined microwaves create a standing wave
• Hot spots are separated by half a wavelength
• Most microwave ovens are around 2400MHz

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Chapter Summary
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• moving conductor in a B field gets a motional
  emf.
• Faradays Law emf -DF/Dt
• Lenzs Law energy conservation
• generators motors utilize F ILB, experience
  back emf
• transformers step ac voltages up or down
• EM waves E B oscillation

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Intensity

• wave intensity in watts/square-meter
• Ex. 5 mW laser is focused to a spot size of
  diameter 1.0 mm.

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Intensity for Different Types of Waves

• Plane Waves Intensity is constant
• Spherical Waves Intensity falls off as inverse
  square

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Energy in EM Waves

• E cB
• u e0 E2 (1/µ0)B2
• Intensity S cu ce0E2 (c/µ0)B2

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Ex. A laser beam has a peak intensity of 150
W/m2. Find the amplitude of the electric and
magnetic fields.

• S cu ce0E2 (c/µ0)B2

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Eddy Currents

• Current induced in metal due to magnetic fields

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calculating emf for loops

• summary
• draw magnetic field lines
• count the number of penetrating lines ( that
  pass through the loop) at two (or more) times
• the emf induced is to the change in of
  penetrating lines per second
• penetrating lines magnetic flux

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• A metallic wire loop is in a uniform magnetic
  field.
• How does the flux change if
• ring moves a little to left or right?
• ring begins to rotate?

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Producing B and E Fields

• Electrical current creates B
• Changing B field creates a circulating E field.
• This E field creates the circulating currents
  observed in wire loops.

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Back emf

• rotating coil in motor experiences an induced emf
  opposite to batterys V
• net voltage V back-emf IR
• I current in motor
• R resistance of motor coil
• back-emf speed of coil, therefore is zero when
  motor starts (or freezes)
• current is large when back-emf is small

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Direct Current (DC) Generators
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• split ring keeps current flowing in only one
  direction
• output can be smoothed

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120 V ac is applied across the primary of a step
down transformer with turns ratio 1/50. How does
the power applied at the primary compare to that
at the secondary? (Assume a lossless transformer)

• Reduced by a factor of 50
• Increased by a factor of 50
• It is the same
• Not enough information

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Application to Power Generation
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• Higher voltage transmission reduces resistive
  heat loss (I2R).
• Ex. Power transmitted thru 10m long wire which
  has 1 ohm resistance.
• At 6V Current V/R 6V/1ohm 6A
• At 60V Current V/R 60V/1ohm 6A