chapter 8 electromagnetic waves

• Displacement current

  Current due to changing electric field, not flow of charges
• Charging of a capacitor

  1. Conduction current through circuit

  2. Displacement current between capacitor plates
• Ampere's circuital law is missing a term to account for magnetic field from changing electric field</b>
• Total current


  Conduction current + Displacement current
• Ampere-Maxwell law: Magnetic field is due to both conduction current and displacement current
• Displacement current has the same physical effects as conduction current
• Displacement current can exist in regions with no conduction current
• Displacement current makes the laws of electricity and magnetism more symmetrical
• Time-varying electric and magnetic fields give rise to each other
• Consequence of symmetry is the existence of electromagnetic waves
• Stationary charges and uniform currents cannot be sources of electromagnetic waves
• Accelerated charges radiate electromagnetic waves
• Oscillating charges produce oscillating electric and magnetic fields that propagate as electromagnetic waves
• Gauss's Law for electricity

  E.dA = Q/ε0
• Gauss's Law for magnetism

  B.dA = 0
• Faraday's Law

  E.dl = -dΦB/dt
• Ampere-Maxwell Law

  B.dl = μ0(i + ε0∂E/∂t)
• Neither stationary charges nor charges in uniform motion (steady currents) can be sources of electromagnetic waves
• How electromagnetic waves are produced


  1. Accelerated charge oscillates

  2. Produces oscillating electric field

  3. Produces oscillating magnetic field

  4. Oscillating E and B fields regenerate each other

  5. Frequency of wave equals frequency of charge oscillation
• Experimental demonstration of electromagnetic waves had to come in the low frequency region (the radio wave region), as in the Hertz's experiment (1887)
• Jagdish Chandra Bose succeeded in producing and observing electromagnetic waves of much shorter wavelength (25 mm to 5 mm)
• Guglielmo Marconi succeeded in transmitting electromagnetic waves over distances of many kilometres, marking the beginning of the field of communication using electromagnetic waves
• Electromagnetic waves

  • Electric and magnetic fields are perpendicular to each other and to the direction of propagation
  • Electric and magnetic fields vary sinusoidally with position and time
• Wave vector k

  Magnitude and direction describe the direction of propagation of the wave
• Angular frequency ω

  ω = ck, where c = 1/√(μ0ε0)
• Frequency ν and wavelength λ

  νλ = c
• Relationship between electric and magnetic fields


  B0 = E0/c
• Velocity of electromagnetic waves in free space or vacuum is an important fundamental constant, with a value of 3×10^8 m/s
• Electromagnetic waves can carry energy from one place to another
• Different animals are sensitive to different ranges of wavelengths, e.g. snakes can detect infrared waves, and the 'visible' range of many insects extends well into the ultraviolet
• The demarcation between different regions of the electromagnetic spectrum is not sharp and there are overlaps
• Waves can be transverse, longitudinal, or surface waves.
• The wavelength is the distance between two consecutive peaks or troughs.
• Transverse waves have perpendicular oscillations to their direction of travel.