A changing electric field produces a magnetic field, and a changing magnetic field produces an electric field—this chain propagates at the speed of light as an electromagnetic wave.
Basic Knowledge
Maxwell’s displacement current: No actual current flows between the plates of a capacitor, but a changing electric field produces a magnetic field as a “displacement current.” This completes the equations of the electromagnetic field.
Electromagnetic wave: A transverse wave that propagates through a vacuum while changing electric and magnetic fields induce each other.
・Speed: c = 1/√(ε₀μ₀) ≈ 3.0 × 10⁸ m/s（speed of light）
・The electric and magnetic fields are perpendicular to each other and to the direction of propagation（transverse wave）
・Frequency f and wavelength λ: c = fλ
Electromagnetic spectrum（in order of decreasing wavelength）:
Radio waves → Microwaves → Infrared → Visible light → Ultraviolet → X-rays → γ rays
Energy of electromagnetic waves (from the photon viewpoint):E = hf = hc/λ（h = 6.63 × 10⁻³⁴ J·s: Planck’s constant）
Electromagnetic wave (electromagnetic wave)（a wave of changing E and B fields. It propagates through a vacuum at c）
Speed of light c（c = 1/√(ε₀μ₀) ≈ 3.0 × 10⁸ m/s）
Displacement current（Maxwell’s hypothesis that a changing electric field produces a magnetic field）
Planck’s constant h（h = 6.63 × 10⁻³⁴ J·s. Photon energy E = hf）
Electromagnetic spectrum（the types of electromagnetic waves arranged continuously from radio waves to γ rays）
Further Exploration (Background and Significance)
In 1865, Maxwell predicted the existence of electromagnetic waves from his equations. Because their speed agreed with the speed of light, he concluded that “light is an electromagnetic wave.” Later, in 1887, Hertz confirmed radio waves experimentally.
The relationship c = 1/√(ε₀μ₀) is profound: electrical and magnetic constants determine the speed of light. Einstein’s special theory of relativity (1905) begins with the principle that the speed of light is invariant.
Electromagnetic-wave energy E = hf is central to quantum theory. Visible light（f ≈ 5 × 10¹⁴ Hz）has E ≈ 2 eV, X-rays have energies in the keV range, and γ rays have energies of MeV or more; this determines the magnitude of their effects on living organisms.
- c = 1/√(ε₀μ₀) ≈ 3.0 × 10⁸ m/s
- Electromagnetic waves: E field, B field, and direction of propagation are mutually perpendicular
- c = fλ（relationship among speed of light, frequency, and wavelength）
- Spectrum: Radio waves→Microwaves→Infrared→Visible→Ultraviolet→X-rays→γ rays
- Photon energy: E = hf
- h = 6.63 × 10⁻³⁴ J·s
- Displacement current completes Maxwell’s equations
Notes (Easily Confused Points)
① The shorter the wavelength, the higher the frequency and energy. ② Electromagnetic waves are transverse waves (their vibrations are perpendicular to the direction of propagation). Sound waves are longitudinal waves. ③ The difference between γ rays and X-rays is their source（γ rays are produced by nuclear reactions, while X-rays are produced by electron deceleration/excitation）, not a clearly separate wavelength range. ④ Electromagnetic waves propagate even through a vacuum (no medium is required).
Practice
- Find the frequency and photon energy of light with wavelength 500 nm（= 5.0 × 10⁻⁷ m）（c = 3.0 × 10⁸ m/s、h = 6.63 × 10⁻³⁴ J·s）.
- List at least three types of electromagnetic waves in order of decreasing wavelength.
- Explain why Maxwell introduced the concept of displacement current.