Electromagnetic Waves Study Notes

Electromagnetic Wave Creation
- Two straight wires connected to the terminals of an AC generator can create an electromagnetic wave.
- Only the electric wave traveling to the right is shown in the diagram.
Magnetic Field Generation
- The current used to generate the electric wave creates a magnetic field.
Radiation Field Representation
- A visual representation shows the wave of the radiation field far from the antenna.
- Speed of Electromagnetic Wave: The speed of an electromagnetic wave in a vacuum is:
- $c = 299,792,458 ext{ m/s}$
Radio Wave Detection
- A radio wave can be detected with a receiving antenna wire that is parallel to the electric field.
Loop Antenna Detection
- With a receiving antenna in the form of a loop, the magnetic field of a radio wave can be detected.

Wave Properties
- Like all waves, electromagnetic waves have a wavelength (BB) and frequency (f) related by:
- c = f imes BB
Electromagnetic Spectrum
- Breakdown of the spectrum in terms of frequency (Hz) and wavelength (m):
- AM Radio: $10^4 ext{ Hz}$
- FM Radio: $10^6 ext{ Hz}$
- Microwaves: $10^{10} ext{ to } 10^{12} ext{ Hz}$
- Infrared: $10^{12} ext{ to } 10^{14} ext{ Hz}$
- Visible Light Range: $4.0 imes 10^{14} ext{ to } 7.9 imes 10^{14} ext{ Hz}$
- Ultraviolet: $10^{15} ext{ to } 10^{16} ext{ Hz}$
- X-rays: $10^{16} ext{ to } 10^{20} ext{ Hz}$
- Gamma Rays: $10^{20} ext{ to } 10^{24} ext{ Hz}$
Example 1: The Wavelength of Visible Light
- Find the range in wavelengths for visible light in the frequency range between:
- $4.0 imes 10^{14} ext{ Hz}$ and $7.9 imes 10^{14} ext{ Hz}$ .
Conceptual Example 2: Diffraction of AM and FM Radio Waves
- Diffraction: The ability of a wave to bend around an obstacle or the edges of an opening.
- Consideration: Would you expect AM or FM radio waves to bend more readily around an obstacle such as a building?

Fixed and Rotating Mirrors
- Diagram includes an observer, fixed mirror, and rotating octagonal mirror.
- The speed of light in a vacuum:
- $c = 299,792,458 ext{ m/s}$
Conceptual Example 3: Looking Back in Time
- A supernova is a violent explosion occurring at the death of certain stars.
- Astronomical Observation: Viewing such an event is akin to looking back in time due to the travel time of the light emitted.
Maxwell's Prediction of the Speed of Light
- Expression demonstrating electromagnetic properties:
- $c = 3.00 imes 10^8 ext{ m/s}$
- Further relation to permittivity and permeability:
- $c = \frac{1}{ ext{√}(ε imes μ)}$
- where:
  - $ε = 8.85 imes 10^{-12} ext{ C}^2/(N imes m^2)$
  - $μ = 4 ext{π} imes 10^{-7} ext{ T} imes m/A$

Energy Carrying Property
- Electromagnetic waves, like water waves, carry energy.
Total Energy Density
- Expression for the total energy density carried by an electromagnetic wave:
- $U = \frac{1}{2}E^2 + \frac{1}{2}B^2$
- where U is total energy, E is electric field, B is magnetic field, and volume is considered.
Power and Energy Relationship
- Total energy (A):
- $P = ext{Total energy} imes A imes t$

Doppler Effect Characteristics
- The Doppler effect occurs in electromagnetic waves, differing from sound waves for two reasons:
- Sound waves require a medium, while electromagnetic waves do not.
- For sound, motion relative to the medium is crucial. For electromagnetic waves, only the relative motion of the source and observer matters.
Example 6: Radar Guns and Speed Traps
- A police car's radar gun emits an electromagnetic wave at a frequency of $8.0 imes 10^9 ext{ Hz}$ .
- Reflection from a speeding car results in a frequency increase of 2100 Hz.
- Calculation to find the car's speed relative to the highway:
- Use Doppler formula:
 - $f' = fs imes \frac{(1 + v{rel}/c)}{(1 - v_{rel}/c)}$
- Determine the speed:
 - Rearranging leads to:
 - $v{rel} ext{ can be approximated as: } v{rel} = \frac{f' - fs}{fs} c$
 - Calculating with provided data gives approximately:
 - $v_{rel} = 39 ext{ m/s}$

Polarized Electromagnetic Waves
- In a linearly polarized wave, the electric field fluctuates along a single direction, while the direction of wave travel remains constant.
- Comparison: Unpolarized light has random electric field directions.
Polarizing Light
- Polarized light may be produced from unpolarized light using polarizing material.
Malus' Law
- Describes light intensity after passing through a polarizer:
- $I = I_0 ext{cos}^2(θ)$
- Where:
  - $I_0$ = intensity before; $I$ = intensity after the analyzer; $θ$ = angle between the transmission axis of the polarizer and the light's electric field direction.
Example 7: Using Polarizers and Analyzers
- To determine the value of $θ$ so that the average intensity of polarized light at the photocell is one-tenth the average intensity of unpolarized light:
- From Malus' law, derive:
- $0.1I0 = I0 ext{cos}^2(θ)$
- $ext{cos}^2(θ) = 0.1$
- $θ = 63.4°$
Crossed Polarizers
- When Polaroid sunglasses are crossed, the intensity of the transmitted light is reduced to zero.
Conceptual Example 8: Third Polarizing Piece
- Question: If a third piece of polarizing material is inserted between the polarizer and analyzer, does light now reach the photocell?
Occurrence of Polarized Light in Nature
- Unpolarized sunlight may interact with molecules resulting in partially polarized light.