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Class 12 Physics Notes

Electromagnetic Waves Class 12 Notes

Complete, exam-ready notes on electromagnetic waves: displacement current and Maxwell's equations, the properties of EM waves, energy and momentum carried, the full electromagnetic spectrum and its applications — written for CBSE boards, JEE and NEET revision.

Class12SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What are electromagnetic waves in one line?

Electromagnetic waves are self-sustaining, transverse oscillations of electric and magnetic fields that travel through empty space at the speed of light, c = 3 × 10⁸ m/s.

Displacement Current and Maxwell's Equations

Displacement current

A changing electric field produces a magnetic field, exactly as a conduction current does. Maxwell introduced the displacement current Id=ε0dΦEdtI_d = \varepsilon_0 \frac{d\Phi_E}{dt} to fix the inconsistency in Ampère's law for a charging capacitor.

  • Conduction current flows through a conductor because of moving charges; displacement current exists wherever the electric flux changes in time.
  • Inside a charging capacitor the conduction current is zero but the displacement current keeps the magnetic field continuous.
  • Maxwell's four equations describe how charges and fields produce the electric and magnetic fields (qualitative for boards; the displacement-current term is the exam focus).

Why Maxwell is on every paper

The symmetric idea — a changing magnetic field makes an electric field (Faraday), a changing electric field makes a magnetic field (Maxwell term) — is the physical origin of self-sustaining EM waves that need no medium.

Properties of Electromagnetic Waves

  • They are transverse: the electric field, magnetic field and direction of propagation are mutually perpendicular.
  • The oscillating E and B fields are in phase and their amplitudes are related by
  • E0=cB0E_0 = cB_0
  • .
  • They travel at speed
  • c=1μ0ε0≈3×108 m/sc = \frac{1}{\sqrt{\mu_0\varepsilon_0}} \approx 3\times 10^8\,\text{m/s}
  • in vacuum.
  • They do not need a medium and carry energy as well as momentum.
c=1μ0ε0,E0B0=cc = \frac{1}{\sqrt{\mu_0\varepsilon_0}},\qquad \frac{E_0}{B_0} = c
Speed of EM waves and field-amplitude relation

Energy, Intensity and Momentum

Energy density

An EM wave stores energy in both fields. The average energy density is shared equally between the electric and magnetic contributions: u=ε0Erms2=12ε0E02u = \varepsilon_0 E_{\text{rms}}^2 = \frac{1}{2}\varepsilon_0 E_0^2.

  • Intensity:
  • I=12cε0E02I = \frac{1}{2} c\varepsilon_0 E_0^2
  • , the average energy crossing unit area per second.
  • Momentum carried:
  • p=Ucp = \frac{U}{c}
  • , which produces radiation (light) pressure on a surface.
  • Radiation pressure on a perfect absorber is
  • Uc/A\frac{U}{c} / A
  • and twice that on a perfect reflector.
I=12cε0E02,p=UcI = \frac{1}{2}c\varepsilon_0 E_0^2,\qquad p = \frac{U}{c}
Intensity and EM momentum

The Electromagnetic Spectrum

  • In order of decreasing wavelength (increasing frequency and energy): radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays.
  • Visible light spans about 400–700 nm, from violet to red.
  • Radio waves: communication; microwaves: radar and oven; infrared: night vision and remote sensing.
  • UV: sterilisation and vitamin-D synthesis; X-rays: medical imaging; gamma rays: nuclear processes and radiotherapy.

Remember the order

A very common board/JEE question asks for the spectrum order. Anchor it as: gamma < X-ray < UV < visible < IR < microwave < radio (gamma is highest energy, shortest wavelength).

Applications of EM Waves

  • AM/FM radio and television broadcast in the radio band; mobile phones use microwaves.
  • Infrared lamps and remote controls; thermal imaging in night vision.
  • X-rays for bone and dental imaging; gamma rays in cancer treatment and the sterilisation of food and medical equipment.
  • Microwave ovens heat food by dielectric heating of water molecules (microwave frequency ≈ 2.45 GHz).

Solved Examples

Example: A plane EM wave has an electric field amplitude E0=3×103 V/mE_0 = 3\times 10^3\,\text{V/m}. Find the amplitude of the magnetic field.

Solution: B0=E0c=3×1033×108=1×10−5 TB_0 = \frac{E_0}{c} = \frac{3\times 10^3}{3\times 10^8} = 1\times 10^{-5}\,\text{T}. The fields are perpendicular to each other and to the direction of travel.

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Displacement current

Id=ε0dΦEdtI_d = \varepsilon_0\frac{d\Phi_E}{dt}

Speed of light

c=1μ0ε0c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}

Field amplitudes

E0=cB0E_0 = cB_0

Average energy density

u=12ε0E02u = \frac{1}{2}\varepsilon_0E_0^2

Intensity

I=12cε0E02I = \frac{1}{2}c\varepsilon_0E_0^2

EM momentum

p=Ucp = \frac{U}{c}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • EM waves are transverse: E ⊥ B ⊥ direction of propagation.
  • E₀/B₀ = c; the fields oscillate in phase.
  • Maxwell's displacement-current term I_d = ε₀ dΦ_E/dt fixes Ampère's law for a charging capacitor.
  • Spectrum order (increasing λ): gamma < X-ray < UV < visible < IR < microwave < radio.
  • Average energy is shared equally between the electric and magnetic fields.

FAQ

Common questions

What is displacement current?

It is the term ε₀ dΦ_E/dt that Maxwell added to Ampère's law: a changing electric flux produces a magnetic field just as a conduction current does. It is non-zero inside a charging capacitor where no charges flow.

Why are electromagnetic waves transverse?

In an EM wave the oscillating electric and magnetic field vectors are perpendicular to each other and to the direction of propagation, which is the definition of a transverse wave.

Which part of the EM spectrum has the highest energy?

Gamma rays have the highest frequency and shortest wavelength, hence the most energy per photon (E = hν).

Can electromagnetic waves travel through a vacuum?

Yes — unlike sound waves, EM waves need no medium. That is why sunlight and radio signals cross empty space.

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