Class 12 · Chapter 8

Electromagnetic Waves

Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.

Electromagnetic Waves Formula Sheet

9 formulas across 3 topics in Electromagnetic Waves.

1 min read

Updated 2026-07-09 · v1.0.0

Displacement Current & Maxwell's Equations

Maxwell noticed Ampère's law was incomplete for circuits with a charging capacitor — displacement current patches this gap and, in doing so, predicts that light itself is an electromagnetic wave.

I(d) = ε₀ (dΦ(E)/dt)

Displacement current

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Maxwell's fix for Ampère's law inside a charging capacitor's gap, where no conduction current flows but the electric field is still changing

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
I(d)	displacement current	A	[A]
Φ(E)	electric flux through the surface	V·m	[ML³T⁻³A⁻¹]

Valid when

Numerically equal to the conduction current charging the capacitor, ensuring current is continuous everywhere in the circuit

Common mistakes

Displacement current is NOT a flow of charge — it's a changing electric field that acts exactly like a current for the purpose of producing a magnetic field

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∮B·dl = μ₀(I + I(d))

Ampère–Maxwell law

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Ampère's circuital law generalised to include displacement current, making it consistent for ALL surfaces bounded by a loop, not just some

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
I	conduction current enclosed	A	[A]

Valid when

This is the corrected, fully general form of Ampère's law used throughout electrodynamics

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Worth remembering

Maxwell's four equations (Gauss's law for E, Gauss's law for B, Faraday's law, Ampère-Maxwell law) together predict electromagnetic waves travelling at exactly the speed of light — this was the first evidence that light IS an electromagnetic phenomenon

Speed, Fields and the Wave Equation

An electromagnetic wave is a self-sustaining oscillation of E and B fields, each perpendicular to the other and to the direction of propagation, travelling at a speed set entirely by the medium's electric and magnetic properties.

c = 1/√(μ₀ε₀)

Speed of light in vacuum

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Falls directly out of combining Maxwell's equations into a wave equation for E and B

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
c	speed of light in vacuumc ≈ 3 × 10⁸ m/s	m/s	[LT⁻¹]

Valid when

This single formula was historic evidence that light is an electromagnetic wave — μ₀ and ε₀ were measured independently from purely electric/magnetic experiments, yet their combination gives exactly the known speed of light

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v = c/n = 1/√(μ ε)

Speed of an electromagnetic wave in a medium

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
n	refractive index of the medium	dimensionless	[M⁰L⁰T⁰]

Valid when

Speed is always ≤ c in any real medium (n ≥ 1)

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E₀/B₀ = c

Relation between the E and B field amplitudes

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Follows directly from Maxwell's equations applied to a plane electromagnetic wave

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
E₀, B₀	peak amplitudes of the electric and magnetic fields	V/m, T	[MLT⁻³A⁻¹], [MT⁻²A⁻¹]

Valid when

E and B oscillate IN PHASE with each other — both are zero together and peak together, only their ratio is fixed by c

Common mistakes

E and B are NOT equal in magnitude — their ratio equals c (a huge number), so E₀ is numerically much larger than B₀ in SI units

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c = νλ

Wave equation for electromagnetic waves

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
ν	frequency	Hz	[T⁻¹]
λ	wavelength	m	[L]

Valid when

Frequency stays fixed by the source when a wave crosses into a new medium; wavelength and speed both change together

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Energy, Intensity & Radiation Pressure

An electromagnetic wave carries real energy and momentum — it can exert measurable pressure on a surface it strikes, doubling if the surface reflects rather than absorbs.

S = (1/μ₀)(E × B) , I(avg) = ½ cε₀E₀²

Poynting vector and average intensity

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The Poynting vector gives the instantaneous energy flux; averaging its magnitude over one cycle for a sinusoidal wave gives the intensity

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
S	Poynting vector — power per unit area, direction of energy flow	W/m²	[MT⁻³]
I(avg)	average intensity of the wave	W/m²	[MT⁻³]

Valid when

S points in the direction of wave propagation, along E × B

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u(avg) = ε₀E(rms)² = ½ε₀E₀²

Average energy density of an electromagnetic wave

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Electric and magnetic fields each contribute equally to the total energy density; the electric contribution alone equals half the total when doubled appropriately

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
u(avg)	average total energy density (electric + magnetic)	J/m³	[ML⁻¹T⁻²]

Valid when

Electric and magnetic energy densities are exactly EQUAL at every instant in an EM wave — neither dominates

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P = I/c (fully absorbed) ; P = 2I/c (fully reflected)

Radiation pressure

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Momentum carried by the EM wave (p = E/c) transferred to the surface; a reflecting surface reverses the wave's momentum, delivering twice the impulse

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
P	radiation pressure	Pa (N/m²)	[ML⁻¹T⁻²]
I	intensity of the incident radiation	W/m²	[MT⁻³]

Valid when

Doubling for a perfect reflector mirrors the same logic as an elastic vs. inelastic collision transferring momentum

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NEET and JEE Main both test the electromagnetic spectrum's ORDER of increasing/decreasing wavelength (radio → microwave → IR → visible → UV → X-ray → gamma) as pure recall — memorise this sequence alongside the formulas above.

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