Electromagnetic Waves

• Displacement Current

  • Concept: Current due to time-varying electric field
  • Formula: $I_d = \varepsilon_0 \frac{d\Phi_E}{dt}$
  • Ampere-Maxwell Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 (I_c + I_d)$
  • Consequence: Solved inconsistency in Ampere's Circuital Law for charging capacitors

• Maxwell's Equations

  • Gauss's Law for Electricity: $\oint \vec{E} \cdot d\vec{A} = \frac{q}{\varepsilon_0}$ (Electric charge source)
  • Gauss's Law for Magnetism: $\oint \vec{B} \cdot d\vec{A} = 0$ (Magnetic monopoles do not exist)
  • Faraday's Law: $\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_B}{dt}$ (Changing magnetic field creates electric field)
  • Ampere-Maxwell Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_c + \mu_0 \varepsilon_0 \frac{d\Phi_E}{dt}$ (Changing electric field creates magnetic field)

• Nature & Properties of EM Waves

  • Production: Produced by accelerating charges
  • Transverse Nature: $\vec{E}$ and $\vec{B}$ fields oscillate perpendicular to each other and to propagation direction
  • Speed in Vacuum: $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 3 \times 10^8 \text{ m/s}$
  • Speed in Medium: $v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}$
  • Amplitude Ratio: $\frac{E_0}{B_0} = c$
  • Energy Density: Equal distribution between electric and magnetic fields
    • Average $u = \frac{1}{2}\varepsilon_0 E_{rms}^2 + \frac{B_{rms}^2}{2\mu_0} = \varepsilon_0 E_{rms}^2$
  • Momentum & Pressure:
    • Momentum carried: $p = \frac{U}{c}$
    • Exerts Radiation Pressure on surfaces

• Electromagnetic Spectrum (Decreasing Wavelength / Increasing Frequency)

  • Radio Waves
    • Wavelength: $> 0.1 \text{ m}$
    • Source: Accelerating charges in conducting wires / aerials
    • Uses: Radio and TV communication, Cellular phones
  • Microwaves
    • Wavelength: $0.1 \text{ m}$ to $1 \text{ mm}$
    • Source: Special vacuum tubes (Klystron, Magnetron)
    • Uses: RADAR systems, Microwave ovens, Satellite communication
  • Infrared Waves (Heat Waves)
    • Wavelength: $1 \text{ mm}$ to $700 \text{ nm}$
    • Source: Hot bodies and molecules
    • Uses: TV remotes, Night vision, Greenhouse effect maintenance, Physical therapy
  • Visible Light
    • Wavelength: $700 \text{ nm}$ to $400 \text{ nm}$
    • Source: Electrons transitioning in atoms at high temperatures
    • Uses: Human vision, Photography, Optical instruments
  • Ultraviolet (UV) Rays
    • Wavelength: $400 \text{ nm}$ to $1 \text{ nm}$
    • Source: Sun, Arc lamps, Very hot bodies
    • Uses: Water purification, Sterilization, LASIK eye surgery, Detecting forged currency
  • X-Rays
    • Wavelength: $1 \text{ nm}$ to $10^{-3} \text{ nm}$
    • Source: High-energy electrons striking a high-atomic-number target
    • Uses: Medical radiography (detecting fractures), Cancer treatment, Crystal structure analysis
  • Gamma ($\gamma$) Rays
    • Wavelength: $< 10^{-3} \text{ nm}$
    • Source: Radioactive decay of atomic nuclei
    • Uses: Cancer radiotherapy, Sterilizing medical equipment, Nuclear research