Electromagnetic Waves Formula Sheet — JEE Main Physics

Q: What are the most important Electromagnetic Waves formulas for JEE Main?

This Electromagnetic Waves formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Basic idea of displacement current, Electromagnetic waves, Their characteristics, Transverse nature (qualitative ideas only), Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses — each shown with the key result and, where useful, a worked example.

Q: Is this Electromagnetic Waves formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

Q: How should I revise Electromagnetic Waves formulas?

Blurt the Electromagnetic Waves formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Every key Electromagnetic Waves formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 5 sub-topics

Basic idea of displacement current
Electromagnetic waves
Their characteristics
Transverse nature (qualitative ideas only)
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses

Displacement Current & Ampere-Maxwell Law

Displacement current

i_{d} = ε_{0} \frac{d Φ _{E}}{d t}

Φ_{E} =

electric flux; a changing

E

acts as a current and makes a

B

Ampere-Maxwell law

\oint B \cdot d l = μ_{0} (i_{c} + i_{d}) = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d Φ _{E}}{d t}

i_{c} =

conduction current

Key facts

▸Outside a charging capacitor: only $i_{c}$ ; between the plates: only $i_{d}$ , and $i_{d} = i_{c}$ .
▸Total current ( $i_{c} + i_{d}$ ) is $continuous$ — gives the same B for any surface.
▸Symmetry: a changing $E$ makes $B$ , just as a changing $B$ makes $E$ (Faraday).

🚫 Examiner Trap · Displacement current

(1)

i_{d}

not

a flow of charge — it's a changing

E

that produces

B

. (2) Between capacitor plates

i_{d} = i_{c}

exactly, so B is continuous across the gap. (3) Maxwell added

i_{d}

to fix Ampere's law — this term

predicts EM waves

. (4)

i_{d} = ε_{0} d Φ_{E} / d t

, NOT

ε_{0} d E / d t

(it's the flux).

Maxwell's Equations & Sources

Maxwell's four equations

Law	Equation	Says
Gauss (E)	$\oint E \cdot d A = q / ε_{0}$	charges make E
Gauss (M)	$\oint B \cdot d A = 0$	no monopoles
Faraday	$\oint E \cdot d l = - \frac{d Φ _{B}}{d t}$	changing B makes E
Ampere-Maxwell	$\oint B \cdot d l = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d Φ _{E}}{d t}$	current + changing E make B

An oscillating charge / antenna radiating electromagnetic waves as expanding wavefronts — An oscillating charge radiates EM waves.

Sources

▸Only $accelerating / oscillating$ charges radiate — static charges and steady currents do NOT.
▸Wave frequency $=$ frequency of the oscillating charge (LC oscillator / antenna).
▸First produced & detected by Hertz (1887).

🚫 Examiner Trap · Maxwell's equations & sources

(1)

\oint B \cdot d A = 0

means

no magnetic monopoles

(B-lines always close). (2) A charge at rest or in

uniform

motion does NOT radiate — only

accelerated

charge does. (3) The wave's frequency equals the source's oscillation frequency, not its amplitude. (4) Faraday and Ampere-Maxwell together let E and B regenerate each other

\Rightarrow

a self-sustaining wave.

Nature of Electromagnetic Waves

Characteristics

▸ $Transverse$ : $E ⊥ B ⊥$ direction of propagation.
▸ $E$ and $B$ oscillate $in phase$ , same frequency; propagation along $E \times B$ .
▸Need $no medium$ (non-mechanical); travel through vacuum at c.

Plane wave (along z)

E_{x} = E_{0} sin (k z - ω t); B_{y} = B_{0} sin (k z - ω t)

k = 2 π / λ

ω = 2 π ν

; E along x, B along y, wave along z

Electric field along x and magnetic field along y, both sinusoidal and in phase, propagating along z — $E$ , $B$ perpendicular and in phase.

Field relation

E_{0} = c B_{0} (E = c B at every instant)

E

is numerically

c

times

B

— but they carry equal energy

🚫 Examiner Trap · Nature of EM waves

(1) EM waves are

transverse

and need

no medium

— unlike sound. (2)

E

and

B

are

in phase

(peak together), NOT

9 0^{\circ}

apart. (3) Propagation is along

E \times B

. (4)

E_{0} = c B_{0}

— at any instant

E / B = c

; don't set

E_{0} = B_{0}

. (5) EM waves are polarisable (transverse).

Speed & Energy of EM Waves

Speed of light

c = \frac{1}{μ _{0} ε _{0}} = 3 \times 1 0^{8} m s^{- 1}

same for all frequencies in vacuum; light IS an EM wave

In a medium

v = \frac{1}{μ ε} = \frac{c}{n}

refractive index

n = μ_{r} ε_{r} = c / v \geq 1

Energy density

u = \frac{1}{2} ε_{0} E^{2} + \frac{B ^{2}}{2 μ _{0}}; u_{E} = u_{B}

the two fields carry

equal

energy

Average energy density

u_{a vg} = \frac{1}{2} ε_{0} E_{0}^{2} = \frac{B _{0}^{2}}{2 μ _{0}} = ε_{0} E_{r m s}^{2}

E_{0}, B_{0} =

peak fields;

E_{r m s} = E_{0} / 2

🚫 Examiner Trap · Speed & energy

(1)

c = 1/ μ_{0} ε_{0}

— independent of frequency and of the source's motion. (2) In a medium

v = c / n < c

;

n = μ_{r} ε_{r}

. (3) Although

E_{0} = c B_{0}

makes E look huge,

u_{E} = u_{B}

exactly (energy split equally). (4)

u_{a vg} = \frac{1}{2} ε_{0} E_{0}^{2}

uses the

\frac{1}{2}

from time-averaging

sin^{2}

Intensity, Momentum & Radiation Pressure

Intensity

I = u_{a vg} c = \frac{1}{2} ε_{0} E_{0}^{2} c = ε_{0} E_{r m s}^{2} c

power per area; point source

I \propto 1/ r^{2}

Momentum delivered

p = \frac{U}{c} (absorbed); p = \frac{2 U}{c} (reflected)

U =

energy delivered to the surface

EM wave hitting an absorbing surface (p=U/c) versus a reflecting surface (p=2U/c) — Reflection delivers twice the momentum.

Comparative: absorbed vs reflected

Surface	Momentum	Pressure
Perfect absorber	$U / c$	$I / c$
Perfect reflector	$2 U / c$	$2 I / c$

Notes

▸EM waves carry both energy and momentum (Nichols & Hull, 1903).
▸Radiation pressure is tiny but real — comet tails point away from the Sun; solar sails.

🚫 Examiner Trap · Intensity & radiation pressure

(1) A

reflector

feels

twice

the momentum/pressure of an absorber (the wave reverses). (2)

I = u_{a vg} c

— multiply energy density by c. (3) Pressure

= I / c

, so it's tiny (c huge). (4) For a point source

I \propto 1/ r^{2}

but the wave speed stays c.

Electromagnetic Spectrum

All bands

c = ν λ = 3 \times 1 0^{8} m s^{- 1}

every band travels at c in vacuum; only

ν, λ

differ

The electromagnetic spectrum from radio (long wavelength) to gamma rays (short wavelength) — Increasing frequency: radio $\to$ $γ$ -rays.

Band	Wavelength	Production
Radio	$> 0.1$ m	accelerating charges in aerials
Microwave	0.1 m–1 mm	klystron / magnetron
Infrared	1 mm–700 nm	molecular vibration
Visible	700–400 nm	electron transitions
Ultraviolet	400–1 nm	inner-shell electrons
X-ray	1 nm–1 $0^{- 3}$ nm	fast electrons hit metal
$γ$ -ray	$< 1 0^{- 3}$ nm	radioactive nuclei

🚫 Examiner Trap · EM spectrum

(1)

All

bands travel at c in vacuum — frequency/wavelength differ, speed does not. (2) Higher

ν

\Rightarrow

shorter

λ

\Rightarrow

higher photon energy (

E = h ν

). (3) Order (increasing

ν

): radio

<

micro

<

<

visible

<

<

X-ray

<

γ

. (4) Visible is a

tiny

slice (400–700 nm).

Properties & Applications of Each Band

Band uses (low

ν

to high

ν

)

Band	Main uses
Radio	TV, AM/FM, cellular
Microwave	radar, speed guns, ovens (water resonance)
Infrared	heating, remotes, night vision, greenhouse
Visible	sight, optical instruments
Ultraviolet	sterilisation, LASIK (ozone absorbs it)
X-ray	medical imaging, crystallography
$γ$ -ray	cancer therapy, sterilising; from nuclei

Atmospheric transmission showing the visible and radio windows where EM waves pass through — Atmosphere transmits mainly visible & radio.

🚫 Examiner Trap · Applications & atmosphere

(1) Ozone absorbs harmful

UV

; C

O_{2}

/water vapour trap

IR

(greenhouse effect). (2) The atmosphere is transparent only in the

visible

and

radio

windows — why optical & radio telescopes work from the ground. (3) Microwave ovens heat

water

(not 'all food equally'). (4) Match band to use: X-ray imaging (penetrates soft tissue),

γ

from nuclei (highest energy).

More JEE Main Physics formula sheets

Frequently Asked Questions

What are the most important Electromagnetic Waves formulas for JEE Main?

This Electromagnetic Waves formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Basic idea of displacement current, Electromagnetic waves, Their characteristics, Transverse nature (qualitative ideas only), Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses — each shown with the key result and, where useful, a worked example.

Is this Electromagnetic Waves formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

How should I revise Electromagnetic Waves formulas?

Blurt the Electromagnetic Waves formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Also useful: all formula sheets · JEE Main previous-year papers · most important chapters.