Lec 12- Physics 1 C

1. Simple Plane Electromagnetic Waves

• A plane wave divides space into two regions, with fields to the left and a wave front moving along the x-axis at speed c
  
  
  c.

• Characteristics:

  • Uniform electric and magnetic fields.

  • The wave is transverse, meaning electric and magnetic fields are perpendicular to the direction of propagation.

2. Gauss's Law and the Plane Wave

• For a plane wave through a rectangular Gaussian surface with no electric charge, Gauss's law requires that electric and magnetic fields are perpendicular to the direction of wave propagation.

3. Faraday's Law and the Plane Wave

• The plane wave in a vacuum must satisfy Faraday’s law:

  • Change in magnetic flux across a region leads to an induced electric field.

  • This requirement ensures the relationship between the electric and magnetic fields.

4. Ampere's Law and the Plane Wave

• Similarly, Ampere’s law ensures a time-changing electric field produces a magnetic field in a vacuum.

• This law also reinforces the relationship between electric and magnetic fields in the wave.

5. Properties of Electromagnetic Waves

• Field Orientation: Electric (E
  
  
  E) and magnetic (B
  
  
  B) fields are perpendicular to each other and the direction of wave propagation.

• Speed: EM waves travel in a vacuum at c
  =
  3.00
  ×
  1
  0
  8
  
  
  
  c=3.00×108 m/s.

• Field Magnitude Relationship: E
  =
  c
  B
  
  
  E=cB.

• Medium: EM waves do not require a medium for propagation.

6. Direction of Propagation

• The direction of propagation is given by the vector product (cross product) of the electric and magnetic fields.

7. Realistic vs. Plane Waves

• Real-world EM waves are often sinusoidal (e.g., from oscillating charges).

• At large distances, sinusoidal waves can be approximated as plane waves.

8. Sinusoidal Wave Equations

• For a sinusoidal wave, amplitude and speed must satisfy specific relationships to maintain wave properties.

9. Electromagnetic Waves in Matter

• In materials like air, water, or glass, EM wave speed depends on the material’s dielectric constant.

• Index of Refraction (n): Ratio of speed of light in a vacuum to speed in the material (n
  =
  c
  v
  
  
  
  n=vc ).

10. Examples of EM Waves in Different Materials

• Calculations for materials with specific dielectric constants:

  • Diamonds: K
    =
    5.84
    
    
    K=5.84

  • Ferrite (ferromagnetic material): K
    =
    10
    
    
    K=10, K
    m
    
    =
    1000
    
    
    Km =1000 (high permeability)

11. Energy in Electromagnetic Waves

• EM waves transport energy, measured by the Poynting vector (power per unit area).

• The magnitude of the Poynting vector represents wave intensity.

12. Electromagnetic Radiation Pressure

• EM waves carry momentum and can exert radiation pressure on surfaces.

• For example, solar panels in space can absorb sunlight, experiencing radiation pressure based on wave intensity.

This guide covers the key concepts and equations from the lecture slides on electromagnetic waves. Review the specific examples and equations provided in your slides for a deeper understanding of each topic