Electromagnetic waves: sources, nature and characteristics
Accelerated charges produce electromagnetic waves: E and B oscillate at right angles to each other and to the direction of travel. In vacuum they move at c = 1/√(μ₀ε₀).
How EM waves are produced
A charge at rest produces only an electric field. A charge moving with constant velocity forms a steady current, which gives a steady magnetic field. An accelerated charge produces both a changing electric field and a changing magnetic field. Each changing field creates the other, and together they travel outward as an electromagnetic (EM) wave. A charge oscillating with frequency ν radiates an EM wave of the same frequency ν. Maxwell predicted these waves in the 1860s, and Hertz produced and detected them in 1887. Jagadish Chandra Bose, working in Kolkata, produced EM waves of much shorter wavelength, 25 mm to 5 mm. Marconi later sent EM waves over distances of many kilometres.
Characteristics of EM waves
- They need no material medium; they travel through vacuum.
- In vacuum, all EM waves travel at the same speed, c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m s⁻¹. This equals the speed of light, so light is an EM wave.
- In a medium of permeability μ and permittivity ε, their speed is v = 1/√(με), which is less than c.
- E and B oscillate in phase, and their amplitudes are related by E₀/B₀ = c.
- They are transverse waves.
- They carry energy from one place to another, as sunlight carries energy from the Sun to the Earth.
- Extra reading, not in your textbook now: EM waves also carry momentum, so they press very lightly on a surface they fall on (radiation pressure).
- They carry no charge, so they are not deflected by electric or magnetic fields.
- For every EM wave in vacuum, c = νλ.
Transverse nature (qualitative idea)
Take an EM wave travelling along the z-axis. Its electric field E oscillates along the x-axis and its magnetic field B along the y-axis. So E, B and the direction of travel are mutually perpendicular. Both fields vibrate at right angles to the direction of travel, so the wave is transverse. The wave travels in the direction of E × B. The fields can be written as E_x = E₀ sin(kz − ωt) and B_y = B₀ sin(kz − ωt), where k = 2π/λ. You need only this picture, not a derivation.
How to draw a plane EM wave
- Draw three axes from one point: x upwards, y slanting towards you, and z to the right.
- Label the z-axis as the direction of propagation, and write c beside it.
- Draw a sine curve in the vertical x-z plane and label it E.
- Draw a second sine curve in the horizontal y-z plane, with its peaks at the same points along z, and label it B.
- Add small arrows from the axis to each curve to show the field directions.
- Mark one wavelength λ along the z-axis.
Worked example: fields and wavelength
A plane EM wave of frequency 30 MHz travels in vacuum. The peak electric field is 48 V m⁻¹. Find (a) the wavelength and (b) the peak magnetic field. (c = 3 × 10⁸ m s⁻¹)
- (a) λ = c/ν = (3 × 10⁸ m s⁻¹) ÷ (30 × 10⁶ Hz) = (3 × 10⁸) ÷ (3 × 10⁷) = 10 m.
- (b) B₀ = E₀/c = 48 V m⁻¹ ÷ (3 × 10⁸ m s⁻¹) = 16 × 10⁻⁸ T = 1.6 × 10⁻⁷ T.
(a) 10 m; (b) 1.6 × 10⁻⁷ T
The sunlight that warms your skin and the signal that reaches a rooftop DTH dish are both EM waves. Both cross empty space at 3 × 10⁸ m s⁻¹ without needing any medium.
2 marks: “Write any four characteristics of electromagnetic waves.” Need no medium; speed c = 1/√(μ₀ε₀) in vacuum; transverse, with E and B perpendicular and in phase; E₀/B₀ = c; carry energy; not deflected by electric or magnetic fields (any four).
3 marks: “How are electromagnetic waves produced? Draw a labelled diagram of a plane EM wave travelling along the z-direction, showing E and B.” Accelerated or oscillating charges give changing E and B fields that sustain each other; diagram with E along x, B along y, propagation along z, in phase, λ marked.
1 marks: “The peak electric field of an EM wave in vacuum is 6 V m⁻¹. What is its peak magnetic field?” B₀ = E₀/c = 6 ÷ (3 × 10⁸) = 2 × 10⁻⁸ T.
E, B and the direction of travel are three right angles, like the edges at the corner of a room. Speed c = 1/√(μ₀ε₀); field ratio E₀/B₀ = c.