Electromagnetic Waves Physics Lesson 33 by Owen Borville 1.10.2026
Electromagnetic waves contain oscillating electric and magnetic fields that propagate at the speed of light (c). These waves were predicted by James Clerk Maxwell, who developed the equation c = 1/√μ0ε0, where μ0 is the permeability of free space and ε0 is the permittivity of free space.
Maxwell's prediction of electromagnetic waves resulted from his development of a complete and symmetric theory of electricity and magnetism: Maxwell's equations.
The symmetry introduced between electric and magnetic fields through Maxwell's displacement current explains the mechanism of electromagnetic wave propagation, in which changing magnetic fields produce changing electric fields and vice versa. Displacement current = Id = ε0dΦE/dt
Although light was already known to be a wave, the nature of the wave was not understood before Maxwell. Maxwell's equations also predicted electromagnetic waves with wavelengths and frequencies outside the range of light. These theoretical predictions were first confirmed experimentally by Heinrich Hertz.
These four equations (including Lorentz force law) cover the major laws of electricity and magnetism:
(1) Gauss's law for electricity = ∫E*dA = Qin/ε0
(2) Gauss's law for magnetism = ∫B*dA = 0
(3) Faraday's law of induction, including Lenz's law = ∫E*dl = -dΦm/dt
(4) Ampere's law in a symmetric formulation that adds another source of magnetism: changing electric fields ∫B*dl = μ0I + ε0 μ0 dΦE/dt
Maxwell's equations predict that the directions of electric and magnetic fields of the wave, and the wave's direction of propagation, are all mutually perpendicular. The electromagnetic wave is a transverse wave.
The wave equation for plane EM waves = ∂²Ey/∂x² = ε0μ0∂²Ey/∂t²
Electromagnetic waves are created by oscillating charges (which radiate whenever accelerated) and have the same frequency as the oscillation. Since the electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.
The strengths of the electric and magnetic parts of the electromagnetic wave are related by the ratio c = E/B which shows that the magnetic field B is very weak compared to the electric field E. Accelerating charges create electromagnetic waves (e.g. an oscillating current in a wire produces electromagnetic waves with the same frequency as the oscillation.)
The relationship between the speed of propagation, wavelength, and frequency for any wave is vw = fλ, where f is the frequency, λ is the wavelength, and c is the speed of light.
The electromagnetic spectrum is separated into many sections, based on the frequency and wavelength, source, and uses of the electromagnetic waves.
Radio waves are electromagnetic waves produced by currents in wires, the lowest frequency electromagnetic waves. Radio waves are classified into many types, depending on their applications, ranging up to microwaves at their highest frequencies.
Infrared radiation is below visible light in frequency and is produced by thermal motion and the vibration and rotation of atoms and molecules. Infrared's lower frequencies overlap with the highest frequency microwaves.
Visible light is mostly produced by electronic transitions in atoms and molecules, and is defined as being detectable by the human eye. Visible light colors vary with frequency, from red at the lowest to violet at the highest.
Ultraviolet radiation has frequencies just above violet in the visible range and is produced mostly by electronic transitions in atoms and molecules.
X-rays are created in high-voltage discharges and by electron bombardment of metal targets. Their lowest frequencies overlap the ultraviolet range but extend to much higher values, overlapping at the high end with gamma rays.
Gamma rays have a nuclear origin and include the highest-frequency electromagnetic radiation of any type.
The energy carried by any wave is proportional to its amplitude squared. For electromagnetic waves, intensity = Iave = (cε0E0^2)/2. Iave is the average intensity in W/m^2 and E0 is the maximum electric field strength of a continuous sinusoidal wave. Iave can also be expressed in terms of the maximum magnetic field strength B0 = Iave = cB0^2/(2μ0) and in terms of both electric and magnetic fields as Iave = E0B0/2μ0.
These three expressions for Iave are all equivalent = Iave = (cε0E0^2)/2 = cB0^2/(2μ0) = E0B0/2μ0
Electromagnetic waves carry momentum and exert radiation pressure. The radiation pressure of an electromagnetic wave is directly proportional to its energy density. The pressure is equal to twice the electromagnetic energy intensity if the wave is reflected and equal to the incident energy intensity if the wave is absorbed.
Radiation pressure = P = I/c = Perfect absorber
Radiation pressure = P = 2I/c = Perfect reflector
The energy flux or Poynting vector = S = 1/μ0 (E * B) describes the directional energy flux (power per unit area) of an electromagnetic field, and indicates the rate and direction energy is transferred by electromagnetic waves, with units of W/m^2. This vector explains energy transport in circuits and radiation, showing that the energy flows outside wires, guided by fields, and into components like resistors, causing them to heat up.
Electromagnetic waves contain oscillating electric and magnetic fields that propagate at the speed of light (c). These waves were predicted by James Clerk Maxwell, who developed the equation c = 1/√μ0ε0, where μ0 is the permeability of free space and ε0 is the permittivity of free space.
Maxwell's prediction of electromagnetic waves resulted from his development of a complete and symmetric theory of electricity and magnetism: Maxwell's equations.
The symmetry introduced between electric and magnetic fields through Maxwell's displacement current explains the mechanism of electromagnetic wave propagation, in which changing magnetic fields produce changing electric fields and vice versa. Displacement current = Id = ε0dΦE/dt
Although light was already known to be a wave, the nature of the wave was not understood before Maxwell. Maxwell's equations also predicted electromagnetic waves with wavelengths and frequencies outside the range of light. These theoretical predictions were first confirmed experimentally by Heinrich Hertz.
These four equations (including Lorentz force law) cover the major laws of electricity and magnetism:
(1) Gauss's law for electricity = ∫E*dA = Qin/ε0
(2) Gauss's law for magnetism = ∫B*dA = 0
(3) Faraday's law of induction, including Lenz's law = ∫E*dl = -dΦm/dt
(4) Ampere's law in a symmetric formulation that adds another source of magnetism: changing electric fields ∫B*dl = μ0I + ε0 μ0 dΦE/dt
Maxwell's equations predict that the directions of electric and magnetic fields of the wave, and the wave's direction of propagation, are all mutually perpendicular. The electromagnetic wave is a transverse wave.
The wave equation for plane EM waves = ∂²Ey/∂x² = ε0μ0∂²Ey/∂t²
Electromagnetic waves are created by oscillating charges (which radiate whenever accelerated) and have the same frequency as the oscillation. Since the electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.
The strengths of the electric and magnetic parts of the electromagnetic wave are related by the ratio c = E/B which shows that the magnetic field B is very weak compared to the electric field E. Accelerating charges create electromagnetic waves (e.g. an oscillating current in a wire produces electromagnetic waves with the same frequency as the oscillation.)
The relationship between the speed of propagation, wavelength, and frequency for any wave is vw = fλ, where f is the frequency, λ is the wavelength, and c is the speed of light.
The electromagnetic spectrum is separated into many sections, based on the frequency and wavelength, source, and uses of the electromagnetic waves.
Radio waves are electromagnetic waves produced by currents in wires, the lowest frequency electromagnetic waves. Radio waves are classified into many types, depending on their applications, ranging up to microwaves at their highest frequencies.
Infrared radiation is below visible light in frequency and is produced by thermal motion and the vibration and rotation of atoms and molecules. Infrared's lower frequencies overlap with the highest frequency microwaves.
Visible light is mostly produced by electronic transitions in atoms and molecules, and is defined as being detectable by the human eye. Visible light colors vary with frequency, from red at the lowest to violet at the highest.
Ultraviolet radiation has frequencies just above violet in the visible range and is produced mostly by electronic transitions in atoms and molecules.
X-rays are created in high-voltage discharges and by electron bombardment of metal targets. Their lowest frequencies overlap the ultraviolet range but extend to much higher values, overlapping at the high end with gamma rays.
Gamma rays have a nuclear origin and include the highest-frequency electromagnetic radiation of any type.
The energy carried by any wave is proportional to its amplitude squared. For electromagnetic waves, intensity = Iave = (cε0E0^2)/2. Iave is the average intensity in W/m^2 and E0 is the maximum electric field strength of a continuous sinusoidal wave. Iave can also be expressed in terms of the maximum magnetic field strength B0 = Iave = cB0^2/(2μ0) and in terms of both electric and magnetic fields as Iave = E0B0/2μ0.
These three expressions for Iave are all equivalent = Iave = (cε0E0^2)/2 = cB0^2/(2μ0) = E0B0/2μ0
Electromagnetic waves carry momentum and exert radiation pressure. The radiation pressure of an electromagnetic wave is directly proportional to its energy density. The pressure is equal to twice the electromagnetic energy intensity if the wave is reflected and equal to the incident energy intensity if the wave is absorbed.
Radiation pressure = P = I/c = Perfect absorber
Radiation pressure = P = 2I/c = Perfect reflector
The energy flux or Poynting vector = S = 1/μ0 (E * B) describes the directional energy flux (power per unit area) of an electromagnetic field, and indicates the rate and direction energy is transferred by electromagnetic waves, with units of W/m^2. This vector explains energy transport in circuits and radiation, showing that the energy flows outside wires, guided by fields, and into components like resistors, causing them to heat up.