30 Outline

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30 Outline

• Maxwells Equations and the Displacement Current
• Electromagnetic Waves
• Polarization

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Maxwells Equations

• Gauss Law E B
• Faradays Law
• Amperes Law

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displacement current

• explains existence of B around E

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EM waves

• accelerating charges produce waves of E and B
• can be pulse or harmonic wave

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dipole radiation
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EM waves

• transverse E perpendicular to B
• E and B are in phase
• speed c fl 3 ? 108 m/s

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Electric Dipole Radiation
Example
I(r 1.0m, angle 90) is 12 W/m2.
I at 2.0m and angle of 30 degrees is
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antennas

• can respond to E or B

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Light

• Light is an electromagnetic wave
• c lf 3 ? 108 m/s
• As light waves travel through space they
• transport energy and/or information
• transport momentum

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EM Waves

• carry energy and momentum, shared equally between
  the electric and magnetic fields.

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Energy and Momentum in EM Waves

• Intensity energy/area/time watts/sq.meter

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Example 50W Bulb

• Assume that 5.00 of the electrical power
  consumed by the bulb is converted to light. The
  average intensity at a distance of r 1.00m
• The rms value of E

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Polarization

• Unpolarized light is the superposition of many
  waves with random direction of E.
• Linearly Polarized light has only one direction
  of E.

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Polarizing Filters

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

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Two Filters (incident light unpolarized)

• 1st reduces intensity by 1/2.
• 2nd reduces according to Malus Law

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Polarization by Scattering and Reflection

• Light scattered at 90 degrees is 100 polarized.

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Summary

• displacement current added to Amperes Law
  completes Maxwell Eqs., which explain light
  properties (transverse EM wave with speed c)
• visible light small segment of spectrum
• energy density and pressure
• polarization by reflection/scattering
• Malus Law

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30-4The Wave Equation for Electromagnetic Waves
Omit
End
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Momentum

• momentum U/c

The total energy received in the time by an
area A
The momentum received
The average force
Radiation pressure
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Example (cont.)
Part (b) 2. Use to find
3. Use to find
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Example Consider a laser that puts out an
average power of P1.0 milliwatt in a beam
having a diameter of 1.0 mm. What is the peak
amplitude of the electric field? The area of the
laser beam is The electromagnetic flux S is
Recall so that Substitution of the
numerical values yields and thus