# Electromagnetic Waves and Spectrum

> Electromagnetic waves and spectrum for JEE Physics: transverse E-B fields, E0 = cB0, Poynting vector, radiation pressure and spectrum order.

- Canonical URL: https://prepelephant.com/topics/jee/physics/electromagnetic-waves-and-spectrum
- Exam / course: JEE · Subject: Physics
- Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team
- First published: 2026-10-02
- Last updated: 2026-10-02
- How to cite: "Electromagnetic Waves and Spectrum", PrepElephant, https://prepelephant.com/topics/jee/physics/electromagnetic-waves-and-spectrum

## 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.