JEE Main Physics · Chapter 17

Electromagnetic Waves

Displacement current, properties of EM waves, intensity, radiation pressure and the EM spectrum.

NCERT Class 12JEE Main: 1 Q per shift 8 min read

1. Chapter at a Glance

Electromagnetic (EM) waves are travelling disturbances of electric and magnetic fields that need no medium. Maxwell showed that a changing electric field creates a magnetic field (through the displacement current), which completes the symmetry between electricity and magnetism and predicts light as an EM wave. The chapter covers displacement current, properties of EM waves, energy and momentum they carry, and the EM spectrum with its uses. It is short and scoring: JEE Main asks one question almost every year.

What JEE asks most
  • Relations E₀ = cB₀ and c = 1/√(μ₀ε₀); direction of propagation E × B.
  • Displacement current in a charging capacitor.
  • Intensity, energy density and radiation pressure.
  • Order of the EM spectrum and uses of each band.

2. Displacement Current

  • Ampère's law fails between the plates of a charging capacitor, where no conduction current flows. Maxwell added the displacement current Id = ε₀ dΦE/dt.
  • Ampère–Maxwell law: ∮B·dl = μ₀(Ic + Id).
  • For a capacitor, Id between the plates equals the conduction current in the wires: Id = C dV/dt.
  • Inside circular plates (radius R), the magnetic field at distance r from the axis is B = μ₀Idr/(2πR²).

3. Properties of EM Waves

  • E and B oscillate in phase, perpendicular to each other and to the direction of travel (transverse waves). Direction of propagation is along E × B.
  • Speed in vacuum c = 1/√(μ₀ε₀) = 3 × 10⁸ m s⁻¹; in a medium v = 1/√(με) = c/n, with n = √(μrεr).
  • E₀/B₀ = c. Example: E = E₀ sin(kx − ωt) ĵ, B = B₀ sin(kx − ωt) k̂ travels along +x.
  • Average energy density u = ½ε₀E₀² (half electric, half magnetic). Intensity I = u c = ½ε₀cE₀².
  • EM waves carry momentum p = U/c. Radiation pressure: I/c for full absorption, 2I/c for full reflection.
  • They are produced by accelerated charges and do not need a medium.
x E (vertical)B (horizontal, dashed) propagation along E × B
In an EM wave, E and B are in phase and perpendicular to each other and to the direction of travel.

4. The Electromagnetic Spectrum

BandApprox. wavelengthSource / detectionUses
Radio waves> 0.1 mOscillating currents in antennasRadio, TV, mobile communication
Microwaves1 mm – 0.1 mKlystron, magnetronRadar, microwave ovens, satellite links
Infrared700 nm – 1 mmHot bodiesRemote controls, night vision, physiotherapy
Visible light400 – 700 nmAtoms (electronic transitions)Vision, photography
Ultraviolet1 – 400 nmSun, arcsSterilisation, detecting forgery; mostly absorbed by ozone
X-rays0.01 – 10 nmFast electrons hitting metalMedical imaging, crystal structure
Gamma rays< 0.01 nmNuclear transitionsCancer treatment, sterilising equipment

Increasing frequency (decreasing wavelength): radio → microwave → infrared → visible → UV → X-ray → gamma.

5. Formula Master Table

QuantityFormula
Speed of lightc = 1/√(μ₀ε₀) = fλ
Field amplitudesE₀ = cB₀
Displacement currentId = ε₀dΦE/dt = C dV/dt
Energy density (average)u = ½ε₀E₀²
IntensityI = ½ε₀cE₀²
Radiation pressureI/c (absorbed); 2I/c (reflected)
Speed in mediumv = c/n

6. Mind Map

EM Waves
Maxwell
  • Displacement current
  • Ampère–Maxwell law
Properties
  • Transverse
  • E₀ = cB₀
  • E × B direction
Energy
  • u = ½ε₀E₀²
  • Intensity
  • Radiation pressure
Spectrum
  • Radio to gamma
  • Uses

7. Tips and Tricks

Shortcuts
  • From E = E₀ sin(kx − ωt): v = ω/k, λ = 2π/k, f = ω/2π.
  • If E is along ĵ and the wave moves along î, then B is along k̂ (ĵ × k̂ = î).
  • Mnemonic for the spectrum by increasing frequency: "Raging Martians Invaded Venus Using X-ray Guns".
  • Electric and magnetic energy densities are equal on average.
Mistakes students make
  • Saying the magnetic field carries less energy because B₀ is numerically small — the energies are equal.
  • Forgetting the factor 2 for radiation pressure on a perfect reflector.
  • Confusing wavelength order with frequency order in the spectrum.

8. Important One-liners

  • EM waves are transverse and need no medium.
  • Accelerated charges produce EM waves.
  • All EM waves travel at the same speed in vacuum.
  • Microwaves are used in radar and ovens.
  • The ozone layer absorbs most of the Sun's ultraviolet radiation.
  • Gamma rays have the highest frequency in the EM spectrum.

9. Solved Numericals: Average to Advanced

Five average-level and five advanced-level problems. Click to reveal each answer and its full working. Take c = 3 × 10⁸ m s⁻¹, ε₀ = 8.85 × 10⁻¹² F m⁻¹ and μ₀ = 4π × 10⁻⁷ T m A⁻¹.

Average level

N1Average

Find the wavelength of a 100 MHz FM radio wave.

Show answer & solution

Concept: λ = c/f.

  1. λ = 3 × 10⁸/10⁸.
  2. = 3 m.

Answer: 3 m

N2Average

The magnetic field amplitude of an EM wave is 2 × 10⁻⁸ T. Find its electric field amplitude.

Show answer & solution

Concept: E₀ = cB₀.

  1. E₀ = 3 × 10⁸ × 2 × 10⁻⁸.
  2. = 6 V m⁻¹.

Answer: 6 V m⁻¹

N3Average

Find the frequency of green light of wavelength 500 nm.

Show answer & solution

Concept: f = c/λ.

  1. f = 3 × 10⁸/(5 × 10⁻⁷).
  2. = 6 × 10¹⁴ Hz.

Answer: 6 × 10¹⁴ Hz

N4Average

A 2 μF capacitor is being charged so that its voltage rises at 10³ V s⁻¹. Find the displacement current between its plates.

Show answer & solution

Concept: Id = C dV/dt.

  1. Id = 2 × 10⁻⁶ × 10³.
  2. = 2 × 10⁻³ A = 2 mA (equal to the charging current).

Answer: 2 mA

N5Average

Light enters glass of refractive index 1.5. Find its speed in glass. If glass is non-magnetic, what is its relative permittivity at this frequency?

Show answer & solution

Concept: v = c/n; n = √(μrεr) with μr = 1.

  1. v = 3 × 10⁸/1.5 = 2 × 10⁸ m s⁻¹.
  2. εr = n² = 2.25.

Answer: 2 × 10⁸ m s⁻¹; 2.25

Advanced level

N6Advanced

An EM wave has E₀ = 100 V m⁻¹. Find its average energy density and intensity.

Show answer & solution

Concept: u = ½ε₀E₀²; I = uc.

  1. u = ½ × 8.85 × 10⁻¹² × 10⁴ ≈ 4.43 × 10⁻⁸ J m⁻³.
  2. I = 4.43 × 10⁻⁸ × 3 × 10⁸ ≈ 13.3 W m⁻².

Answer: about 4.4 × 10⁻⁸ J m⁻³; about 13.3 W m⁻²

N7Advanced

Light of intensity 1000 W m⁻² falls normally on a 2 m² surface. Find the radiation pressure and force if the surface (a) absorbs all the light, (b) reflects all of it.

Show answer & solution

Concept: absorbed P = I/c; reflected P = 2I/c; F = PA.

  1. (a) P = 1000/(3 × 10⁸) ≈ 3.33 × 10⁻⁶ Pa; F = 6.67 × 10⁻⁶ N.
  2. (b) P = 6.67 × 10⁻⁶ Pa; F ≈ 1.33 × 10⁻⁵ N.

Answer: (a) 3.3 μPa, 6.7 μN; (b) 6.7 μPa, 13.3 μN

N8Advanced

The electric field of a wave in vacuum is E = 30 sin(2π × 10⁶ t − kx) V m⁻¹. Find its wavelength, k and the amplitude of the magnetic field.

Show answer & solution

Concept: f from ω; λ = c/f; k = 2π/λ; B₀ = E₀/c.

  1. f = 10⁶ Hz ⇒ λ = 3 × 10⁸/10⁶ = 300 m.
  2. k = 2π/300 ≈ 0.021 rad m⁻¹.
  3. B₀ = 30/(3 × 10⁸) = 10⁻⁷ T.

Answer: 300 m; about 0.021 m⁻¹; 10⁻⁷ T

N9Advanced

Sunlight reaching Earth has an intensity of about 1.4 kW m⁻². Estimate the amplitudes of its electric and magnetic fields.

Show answer & solution

Concept: I = ½ε₀cE₀² ⇒ E₀ = √(2I/ε₀c).

  1. ε₀c = 8.85 × 10⁻¹² × 3 × 10⁸ = 2.655 × 10⁻³.
  2. E₀ = √(2800/2.655 × 10⁻³) = √(1.055 × 10⁶) ≈ 1.03 × 10³ V m⁻¹.
  3. B₀ = E₀/c ≈ 3.4 × 10⁻⁶ T.

Answer: about 1030 V m⁻¹; about 3.4 μT

N10Advanced

A capacitor with circular plates of radius 10 cm is being charged by a current of 0.15 A. Find the magnetic field between the plates at 5 cm from the axis.

Show answer & solution

Concept: only the fraction r²/R² of the displacement current is enclosed: B(2πr) = μ₀Idr²/R².

  1. Id = 0.15 A (equals the charging current).
  2. B = μ₀Idr/(2πR²) = 4π × 10⁻⁷ × 0.15 × 0.05/(2π × 0.01).
  3. = 2 × 10⁻⁷ × 0.0075/0.01 = 1.5 × 10⁻⁷ T.

Answer: 1.5 × 10⁻⁷ T

10. PYQ-pattern Questions with Solutions

These questions are original and modelled on concepts frequently tested in JEE Main.

Q1Easy

Which of the following has the shortest wavelength?

  1. Microwaves
  2. Infrared
  3. X-rays
  4. Gamma rays
Show solution

Gamma rays have the highest frequency and hence the shortest wavelength.

Answer: (D)

Q2Easy

The waves used in radar systems are:

  1. Infrared
  2. Ultraviolet
  3. Microwaves
  4. X-rays
Show solution

Microwaves travel in straight lines, pass through clouds and reflect from aircraft — ideal for radar.

Answer: (C)

Q3Medium

An EM wave moves along +z with its electric field along +x. The magnetic field is along:

  1. +x
  2. +y
  3. −y
  4. +z
Show solution

E × B must point along +z: î × ĵ = k̂, so B is along +y.

Answer: (B)

Q4Hard

In an EM wave, the average energy densities associated with the electric and magnetic fields are:

  1. Electric larger
  2. Magnetic larger
  3. Equal
  4. In the ratio c : 1
Show solution

½ε₀E² = B²/2μ₀ because E = cB and c² = 1/μ₀ε₀; so they are equal.

Answer: (C)

Q5Numerical

An EM wave has E₀ = 9 V m⁻¹. Find B₀ in units of 10⁻⁸ T.

Show solution

B₀ = 9/(3 × 10⁸) = 3 × 10⁻⁸ T.

Answer: 3

Q6Medium

The displacement current exists between capacitor plates because of:

  1. Flow of electrons across the gap
  2. A changing electric field
  3. A constant electric field
  4. A changing magnetic field only
Show solution

Id = ε₀dΦE/dt arises from the time-varying electric flux; no charge crosses the gap.

Answer: (B)

11. Quick Revision Summary

Remember before the exam
  • Id = ε₀dΦE/dt; equals the conduction current for a capacitor.
  • c = 1/√(μ₀ε₀); E₀ = cB₀; propagation along E × B.
  • u = ½ε₀E₀², I = ½ε₀cE₀²; pressure I/c or 2I/c.
  • Spectrum by frequency: radio < micro < IR < visible < UV < X < gamma.
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