Electromagnetic Wave
An electromagnetic wave is a self-propagating transverse wave consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation. Predicted theoretically by James Clerk Maxwell in 1865 and confirmed experimentally by Heinrich Hertz in 1887, electromagnetic waves require no medium and travel at the speed of light (3 × 10⁸ m/s) in vacuum. The electromagnetic spectrum spans radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays — all governed by the same wave equations.
Key Formula
c = 1 / √(μ₀ε₀) = f × λ
LaTeX: c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = f\lambda
| Symbol | Meaning | Unit |
|---|---|---|
| c | Speed of electromagnetic wave in vacuum | 3 × 10⁸ m/s |
| μ₀ | Permeability of free space | 4π × 10⁻⁷ T·m/A |
| ε₀ | Permittivity of free space | 8.85 × 10⁻¹² F/m |
| f | Frequency of the wave | Hertz (Hz) |
| λ | Wavelength | Metre (m) |
Worked Example
Problem
An FM radio station broadcasts at a frequency of 98.3 MHz. Calculate the wavelength of the radio waves in vacuum.
Solution
Step 1: Convert frequency to standard form. f = 98.3 MHz = 98.3 × 10⁶ Hz = 9.83 × 10⁷ Hz Step 2: Use the relationship c = fλ → λ = c/f. c = 3 × 10⁸ m/s Step 3: Calculate wavelength. λ = (3 × 10⁸) / (9.83 × 10⁷) λ = 3.052 m
Answer
Wavelength of FM radio wave = 3.05 m
The Electromagnetic Spectrum: Frequency, Wavelength and Applications
| Type | Frequency Range | Wavelength Range | Example Application |
|---|---|---|---|
| Radio waves | 3 Hz – 300 MHz | 1 mm – 100,000 km | AM/FM broadcasting, WiFi |
| Microwaves | 300 MHz – 300 GHz | 1 mm – 1 m | Radar, microwave ovens, 5G |
| Infrared | 300 GHz – 400 THz | 700 nm – 1 mm | Thermal imaging, remote controls |
| Visible light | 400 THz – 800 THz | 380 nm – 750 nm | Human vision, photography |
| Ultraviolet | 800 THz – 30 PHz | 10 nm – 380 nm | Sterilisation, UV spectroscopy |
| X-rays | 30 PHz – 30 EHz | 0.01 nm – 10 nm | Medical imaging, security scans |
Interactive Tools
PhET Radio Waves and Electromagnetic Fields
Visualise how oscillating charges produce electromagnetic waves
Open ToolWolfram Alpha — EM Wave Calculations
Compute EM wave properties: wavelength, frequency, energy
Open ToolKhan Academy — Electromagnetic Waves
Conceptual introduction to EM waves and the electromagnetic spectrum
Open Tool
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Related Terms
Maxwell's Equations
Maxwell's Equations are a set of four partial differential equations formulated by James Clerk Maxwell (1861–1865) that completely describe the behaviour of electric and magnetic fields and their interactions with matter and charge. They unify electricity, magnetism, and optics into a single coherent theory and predicted the existence of electromagnetic waves travelling at the speed of light. Maxwell's Equations are among the greatest achievements in theoretical physics and form the foundation of classical electrodynamics, modern optical theory, and electrical engineering.
Alternating Current
Alternating current (AC) is an electric current that periodically reverses direction, in contrast to direct current which flows only in one direction. The magnitude and direction of AC vary sinusoidally with time at a specific frequency — 50 Hz in India and most of the world, 60 Hz in North America. AC is the standard form of electrical power delivered to homes and industries because it can be efficiently stepped up or down in voltage using transformers, making long-distance transmission economical.
Faraday's Law of Induction
Faraday's Law of Induction states that the electromotive force (EMF) induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop. This fundamental law explains how changing magnetic fields produce electric currents, forming the basis of electric generators, transformers, and induction motors. It was discovered experimentally by Michael Faraday in 1831 and independently by Joseph Henry around the same time.
"Electromagnetic" combines Greek "elektron" (amber, source of static electricity) and "magnetes" (from Magnesia, the mineral source of lodestone). "Wave" from Old English "waefan". The term was established by Maxwell in his 1865 paper "A Dynamical Theory of the Electromagnetic Field".