JEE Mains Physics · Teaching notes

Electromagnetic Waves — JEE Mains Physics

Electromagnetic Waves has 108 past-year questions from 2021 to 2026, and 14 of them ask for a number rather than an option. It is a short chapter in which most questions need a single relation, such as E₀ = cB₀, I = ½cε₀E₀² or v = c/√(μᵣεᵣ), and then a careful cross product for a direction. About a third are about the two fields of the wave themselves, and the spectrum questions are pure recall of order, sources and uses. Marks are lost on factors and directions: B written as cE instead of E/c, the average energy split wrongly between the two fields, a mirror given I/c instead of 2I/c, or the cross product taken in the wrong order.

Every subtopic, worked example, formula and trap in one printable document — answers shown, ready to share.

All 108 past questions JEE Mains Physics strategy JEE Mains home

Subtopic notes

Formula & revision sheet

8 formulas · 3 reference tables · 39 gotchas across all subtopics — the exam-eve cheat-sheet

Displacement Current, Maxwell's Equations and Wave Speed

Formulas (2)

Displacement current in a capacitor · Displacement current $i_d = \varepsilon_0\frac{d\Phi_E}{dt} = C\frac{dV}{dt}, \qquad \frac{(j_c)_0}{(j_d)_0} = \frac{\sigma}{\varepsilon_0\omega}$
Speed of electromagnetic waves in vacuum and in a medium · Wave speed $c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}, \qquad v = \frac{c}{\sqrt{\mu_r\varepsilon_r}} = \frac{\omega}{k}, \qquad n = \sqrt{\mu_r\varepsilon_r}$

Reference tables (1)

Maxwell's four equations and their names5 rows

Law	Equation	What it says
Gauss's law for electricity	$\oint \vec E\cdot d\vec A = q/\varepsilon_0$	The electric flux out of a closed surface is the enclosed charge divided by ε₀.
Gauss's law for magnetism	$\oint \vec B\cdot d\vec A = 0$	Magnetic field lines close on themselves; there are no magnetic monopoles.
Faraday's law of induction	$\oint \vec E\cdot d\vec l = -\dfrac{d\Phi_B}{dt}$	A changing magnetic flux induces an electric field around a loop.
Ampere-Maxwell law	$\oint \vec B\cdot d\vec l = \mu_0 i_c + \mu_0\varepsilon_0\dfrac{d\Phi_E}{dt}$	A conduction current and a changing electric flux both produce a magnetic field.
Ampere's circuital law	$\oint \vec B\cdot d\vec l = \mu_0 I$	The steady-current special case, with no changing electric flux. Without the displacement term it fails across the gap of a charging capacitor.

A closed-surface integral (dA) means a Gauss law; a loop integral (dl) means Faraday or Ampere-Maxwell.

Watch out for (10)

The displacement current equals the conduction current
→ Displacement current in a capacitor
A surface that covers part of the gap takes its share
→ Displacement current in a capacitor
Use ω, not f, in σ/ε₀ω
→ Displacement current in a capacitor
Plain Ampere's law is the steady-current law
→ Maxwell's four equations and their names
Read the integral before the symbols
→ Maxwell's four equations and their names
A steady source gives a steady field
→ Maxwell's four equations and their names
Take the speed from the phase, not c
→ Speed of electromagnetic waves in vacuum and in a medium
A magnetic medium needs μᵣ too
→ Speed of electromagnetic waves in vacuum and in a medium
Square the index, do not double it
→ Speed of electromagnetic waves in vacuum and in a medium
The frequency stays the same in a medium
→ Speed of electromagnetic waves in vacuum and in a medium

E and B Fields of a Plane Wave

Formulas (3)

Writing the magnetic field of a wave from its electric field · One field from the other $\vec B = \frac{\vec k \times \vec E}{\omega}, \qquad B_0 = \frac{E_0}{c}, \qquad \hat n = \hat E \times \hat B$
Electric and magnetic fields at one point of a wave · Fields at a point $|\vec B| = \frac{|\vec E|}{c}, \qquad \hat B = \hat n \times \hat E, \qquad \frac{E_0}{H_0} = \sqrt{\frac{\mu_0}{\varepsilon_0}} \approx 377\ \Omega$
Electric and magnetic forces on a charge in a wave · Forces on a moving charge $F_e = qE_0, \qquad F_m = qvB_0 = \frac{qvE_0}{c}, \qquad \frac{F_e}{F_m} = \frac{c}{v}$

Watch out for (10)

The order of the cross product matters
→ Writing the magnetic field of a wave from its electric field
B keeps the phase of E
→ Writing the magnetic field of a wave from its electric field
Divide by c, do not multiply
→ Writing the magnetic field of a wave from its electric field
Travel along −x flips a sign
→ Writing the magnetic field of a wave from its electric field
The frequency is a distractor
→ Electric and magnetic fields at one point of a wave
B over E is 1/c, not c
→ Electric and magnetic fields at one point of a wave
E₀/B₀ is c, but E₀/H₀ is 377 Ω
→ Electric and magnetic fields at one point of a wave
Neither field lies along the travel direction
→ Electric and magnetic fields at one point of a wave
Use B₀ = E₀/c in the magnetic force
→ Electric and magnetic forces on a charge in a wave
The electric force is the larger one
→ Electric and magnetic forces on a charge in a wave

Energy, Intensity and Radiation Pressure

Formulas (3)

Energy density of an electromagnetic wave · Energy density $u_E = \tfrac{1}{2}\varepsilon_0E^{2} = u_B = \frac{B^{2}}{2\mu_0}, \qquad \langle u\rangle = \tfrac{1}{2}\varepsilon_0E_0^{2} = \frac{B_0^{2}}{2\mu_0}$
Intensity of an electromagnetic wave · Intensity $I = \tfrac{1}{2}c\varepsilon_0E_0^{2} = \frac{cB_0^{2}}{2\mu_0}, \qquad I = \frac{\eta P}{4\pi r^{2}}$
Momentum and radiation pressure of light · Radiation pressure $p = \frac{U}{c}, \qquad P_{\text{absorbed}} = \frac{I}{c}, \qquad P_{\text{reflected}} = \frac{2I}{c}, \qquad F = P_{\text{rad}}A$

Watch out for (12)

½ε₀E₀² is the total average, not the electric share
→ Energy density of an electromagnetic wave
Do not add the magnetic term again
→ Energy density of an electromagnetic wave
The magnetic share is B²/2μ₀, not μ₀B²/2
→ Energy density of an electromagnetic wave
The frequency does not change the average energy
→ Energy density of an electromagnetic wave
Only the radiated power counts
→ Intensity of an electromagnetic wave
Intensity depends on distance, not direction
→ Intensity of an electromagnetic wave
The ½ goes with the peak field
→ Intensity of an electromagnetic wave
The field goes as the square root of the intensity
→ Intensity of an electromagnetic wave
A reflector feels twice the push
→ Momentum and radiation pressure of light
The exposure time does not change the force
→ Momentum and radiation pressure of light
Zero rest mass does not mean zero momentum
→ Momentum and radiation pressure of light
Use the area the light sees
→ Momentum and radiation pressure of light

Electromagnetic Spectrum: Order, Sources and Uses

Reference tables (2)

Order and wavelength ranges of the electromagnetic spectrum7 rows

Band	Wavelength range	Frequency range	Photon energy
γ-rays	shorter than 10⁻³ nm	above 3 × 10²⁰ Hz	above 1.24 MeV
X-rays	1 nm to 10⁻³ nm	3 × 10¹⁷ to 3 × 10²⁰ Hz	1.24 keV to 1.24 MeV Shorter than ultraviolet, longer than γ-rays.
Ultraviolet	400 nm to 1 nm	7.5 × 10¹⁴ to 3 × 10¹⁷ Hz	3.1 eV to 1.24 keV
Visible	700 nm to 400 nm	4.3 × 10¹⁴ to 7.5 × 10¹⁴ Hz	1.8 eV to 3.1 eV
Infrared	1 mm to 700 nm	3 × 10¹¹ to 4.3 × 10¹⁴ Hz	1.24 meV to 1.8 eV
Microwaves	0.1 m to 1 mm	3 × 10⁹ to 3 × 10¹¹ Hz	12.4 µeV to 1.24 meV
Radio waves	longer than 0.1 m	below 3 × 10⁹ Hz	below 12.4 µeV

Wavelength rises down the table; frequency and photon energy fall.

Sources, detectors and uses of each band7 rows

Band	Produced by	Detected by	Main uses
Radio waves	Rapid acceleration and deceleration of electrons in aerials	Receiving aerials	Radio and television broadcasting, mobile communication
Microwaves	Klystron valve, magnetron valve, Gunn diode	Point-contact diodes	Radar, aircraft navigation, microwave ovens Klystron and magnetron both mean microwaves.
Infrared	Vibrations of atoms and molecules; hot bodies	Thermopiles, bolometers, infrared photographic film	Physiotherapy heat lamps, greenhouse effect, remote controls, seeing through fog
Visible light	Electrons in atoms dropping between outer energy levels	The eye, photocells, photographic film	Vision, photography, optical communication
Ultraviolet	Electron transitions in atoms; the sun and arc lamps	Photocells, photographic film	Sterilising surgical instruments, purifying water, Lasik eye surgery
X-rays	Inner-shell electron transitions; fast electrons striking a metal target	Photographic film, Geiger tubes, ionisation chambers	Medical diagnosis, cancer treatment, study of crystal structure A metal target hit by fast electrons gives X-rays, not γ-rays.
γ-rays	Radioactive decay of nuclei	Photographic film, Geiger tubes, ionisation chambers	Destroying cancer cells, sterilising medical equipment

The source sets the band: the deeper inside the atom, the shorter the wavelength.

Watch out for (7)

γ-rays are shorter than X-rays
→ Order and wavelength ranges of the electromagnetic spectrum
More energetic means shorter wavelength
→ Order and wavelength ranges of the electromagnetic spectrum
Convert each end of a band separately
→ Order and wavelength ranges of the electromagnetic spectrum
Inner shells give X-rays, the nucleus gives γ-rays
→ Sources, detectors and uses of each band
Radar uses microwaves
→ Sources, detectors and uses of each band
The greenhouse effect is infrared
→ Sources, detectors and uses of each band
Ultraviolet sterilises, X-rays image
→ Sources, detectors and uses of each band

PYQ weightage by concept

11 concepts · 108 PYQs — where the marks actually sit, so you know what to drill first

Displacement Current, Maxwell's Equations and Wave Speed28 PYQs · 26%

Concept	PYQs	Share
Speed of electromagnetic waves in vacuum and in a medium	15	14%
Displacement current in a capacitor	7	6%
Maxwell's four equations and their names	6	6%

E and B Fields of a Plane Wave34 PYQs · 31%

Concept	PYQs	Share
Electric and magnetic fields at one point of a wave	16	15%
Writing the magnetic field of a wave from its electric field	14	13%
Electric and magnetic forces on a charge in a wave	4	4%

Energy, Intensity and Radiation Pressure30 PYQs · 28%

Concept	PYQs	Share
Intensity of an electromagnetic wave	13	12%
Energy density of an electromagnetic wave	10	9%
Momentum and radiation pressure of light	7	6%

Electromagnetic Spectrum: Order, Sources and Uses16 PYQs · 15%

Concept	PYQs	Share
Order and wavelength ranges of the electromagnetic spectrum	9	8%
Sources, detectors and uses of each band	7	6%

Test yourself on Electromagnetic Waves

20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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