Electromagnetic Waves and Spectrum
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Direct answer
Electromagnetic waves carry energy through mutually perpendicular, in-phase oscillating electric and magnetic fields, both transverse to the direction of propagation, travelling in vacuum at c = 1/sqrt(mu(0) epsilon(0)) = 3 × 10^8 m/s with the fixed amplitude ratio E(0) = c B(0). The Poynting vector S = (1/mu(0)) E × B gives the intensity (here averaging to I = (1/2) epsilon(0) c E(0)^2 for sinusoidal waves), and the radiation pressure on a perfectly absorbing surface is I/c, doubling to 2I/c on a perfect reflector. The spectrum, ordered by rising frequency, runs radio, microwave, infrared, visible (700 to 400 nanometres), ultraviolet, X-rays and gamma rays — same physics, same speed in vacuum, different wavelengths and the technologies built on them.
What you must remember
- Structure of the wave: E, B and propagation direction are mutually perpendicular; E and B oscillate in phase; both fields are transverse, which is why light can be polarised.
- Speed and amplitude links: c = 1/sqrt(mu(0) epsilon(0)) = 3 × 10^8 m/s in vacuum; in a medium v = 1/sqrt(mu epsilon); E(0)/B(0) = c at every instant.
- Energy carriage: energy density splits equally between fields, u(E) = (1/2) epsilon(0) E^2 and u(B) = B^2/(2 mu(0)); average intensity I = (1/2) epsilon(0) c E(0)^2 falls off as 1/r^2 from a point source.
- Poynting vector: S = (1/mu(0)) E × B points along propagation and gives energy flow per unit area per second — its direction is a favourite Main assertion.
- Radiation pressure: p = I/c on a perfect absorber, 2I/c on a perfect reflector; sunlight's pressure near earth is about 4.5 × 10^-6 Pa.
- Production map: oscillating circuits (radio), klystron and magnetron (microwave), hot bodies and molecular vibrations (infrared), atomic electrons (visible, UV), fast electrons stopped in metal (X-rays), nuclear transitions (gamma).
- Spectrum anchors: visible 700 nm (red) to 400 nm (violet); infrared sensed as heat by skin and emitted by every warm body; microwaves serve radar and communication links — one spectrum, one speed c in vacuum.
- Pattern note: Main asks order-of-spectrum, E(0)–B(0) conversion and intensity/pressure formulae; Advanced adds displacement current reasoning and energy-density equality proofs.
Converting between the wave's two faces
A plane electromagnetic wave in vacuum has E(0) = 60 V/m — the sort of number JEE hands you cold. Then B(0) = E(0)/c = 60/(3 × 10^8) = 2 × 10^-7 T; the average intensity I = (1/2) epsilon(0) c E(0)^2 = 0.5 × 8.85 × 10^-12 × 3 × 10^8 × 3600 ≈ 4.8 W/m^2; on a black surface this exerts pressure I/c ≈ 1.6 × 10^-8 Pa; on a mirror it doubles — all from two ratios, E(0)/B(0) = c and pressure = I/c.
The spectrum reasoning runs on the same economy. A 1 MHz AM signal has lambda = c/f = 300 m; an FM signal at 100 MHz has 3 m; a microwave oven's 2.45 GHz gives about 12 cm, chosen to penetrate food while being absorbed by water molecules. X-rays and gamma rays overlap in wavelength — the distinction is origin, not wavelength, and saying so precisely is what the exam rewards.
Where students slip
E and B are in phase — many candidates sketch them a quarter-cycle apart by analogy with velocity and position in SHM; they are not, and the error shows up in diagram-based questions. Second, the amplitude ratio is E(0) = c B(0), so B's numerical value in tesla is always small; computing B(0) = E(0)/c in the wrong direction (multiplying) inflates it by 10^16 and should trigger an immediate sanity check. Third, radiation pressure on a reflector is 2I/c because momentum reverses on reflection; answering I/c halves the mark. Fourth, ordering the spectrum by wavelength while the question lists frequencies (or vice versa) reverses everything: gamma has the smallest wavelength and the highest frequency, radio the opposite. And all electromagnetic waves share speed c in vacuum — answers giving light a different vacuum speed from X-rays are wrong on principle.
Frequently asked questions
How are the electric and magnetic fields oriented in an electromagnetic wave?
Mutually perpendicular, each perpendicular to the direction of travel, oscillating in phase — a transverse wave, which is why it can be polarised.
What relates the amplitudes of E and B in vacuum?
E(0) = c B(0); the electric field amplitude in volts per metre is always c times the magnetic amplitude in tesla.
What does the Poynting vector represent?
The instantaneous energy flux, S = (1/mu(0)) E × B, whose magnitude is energy crossing unit area per second and whose direction is the propagation direction.
Why is radiation pressure on a mirror double that on a black surface?
An absorber takes the photon momentum I/c per second, a reflector reverses it, transferring twice the momentum and feeling 2I/c.
How are X-rays and gamma rays distinguished despite overlapping wavelengths?
By origin: X-rays from energetic electrons decelerating or electronic transitions, gamma rays from nuclear or particle decays — the production mechanism, not the wavelength, separates them.