Electromagnetic Waves — Physics Class 12 Notes (CBSE & HBSE)
Free NCERT Physics notes for Electromagnetic Waves (Class 12) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Electromagnetic Waves (CBSE & HBSE)
CBSE focuses on Maxwell displacement current derivation, EM wave properties including c=1/sqrt(e0m0), and the EM spectrum applications. HBSE tests displacement current, transverse nature of EM waves, EM spectrum, and E0/B0=c numericals.
Displacement Current and Maxwell Equations
Maxwell Displacement Current
Displacement Current was introduced by James Clerk Maxwell to resolve an inconsistency in Ampere circuital law for time-varying electric fields.
Inconsistency in Ampere Law
Ampere law: ∮B⃗·dl⃗ = μ₀I_c works for steady currents but fails for a charging capacitor. When a capacitor charges, conduction current I_c flows in wires, but NO conduction current crosses the capacitor gap yet a magnetic field exists there.
Two Amperian loops around the capacitor:
- Loop through wire: encloses I_c => gives B != 0
- Loop through gap: encloses 0 current => gives B = 0
This contradiction needed resolution.
Maxwell Resolution
Maxwell proposed that the changing electric field between plates acts like a current:
I_d = ε₀ dPhi_E/dt
For a capacitor with charge Q, plate area A:
- E = Q/(ε₀A) between plates
- Phi_E = E*A = Q/ε₀
- I_d = ε₀ d(Q/ε₀)/dt = dQ/dt = I_c (Equal!)
Modified Ampere-Maxwell Law
∮B⃗·dl⃗ = μ₀(I_c + I_d) = μ₀I_c + μ₀ε₀ dPhi_E/dt
Both loops now give the same magnetic field.
Maxwell Four Equations
| Equation | Integral Form | Physical Meaning |
|---|---|---|
| Gauss Law (E) | ∮E·dA = Q/ε₀ | Charges create E-field |
| Gauss Law (B) | ∮B·dA = 0 | No magnetic monopoles |
| Faraday Law | ∮E·dl = -dPhi_B/dt | Changing B creates E |
| Ampere-Maxwell | ∮B·dl = μ₀I + μ₀ε₀ dPhi_E/dt | Current or changing E creates B |
Displacement vs Conduction Current
| Property | Conduction I_c | Displacement I_d |
|---|---|---|
| Cause | Moving free charges | Changing electric flux |
| Conductor needed | Yes | No - exists in vacuum |
| Produces B field | Yes | Yes |
| Formula | I_c = dQ/dt | I_d = ε₀ dPhi_E/dt |
Key insight: Displacement current ensures total current is continuous across any cross section, even across a capacitor gap. This led Maxwell to predict electromagnetic waves.
Properties of EM Waves and EM Spectrum
Electromagnetic Waves Properties
Nature and Generation
EM waves are generated by accelerating charged particles. They consist of oscillating E and B fields perpendicular to each other and to the direction of propagation.
Mathematical Form
For an EM wave traveling in +x direction:
E_y = E₀ sin(kx - ωt) and B_z = B₀ sin(kx - ωt)
where k = 2π/λ (wave number), ω = 2πf (angular frequency).
Key relation: E₀/B₀ = c (electric to magnetic field ratio equals speed of light)
Speed Derivation
From Maxwell equations in vacuum:
c = 1/√(ε₀μ₀) = 1/√(8.854x10^-12 x 4πx10^-7)
c = 3x10^8 m/s which exactly matches experimentally known speed of light!
This proved that light is an electromagnetic wave.
Speed in a Medium
v = c/n = 1/√(εμ) where n = refractive index, ε = permittivity, μ = permeability
Energy and Intensity
- Equal energy stored in E and B fields: u_E = u_B = ½e₀E^2
- Average intensity: I = ½e₀E₀^2 c = cB₀^2/(2μ₀)
- Radiation pressure (absorption): P = I/c
Properties Table
| Property | Description |
|---|---|
| Nature | Transverse wave |
| E, B, propagation | Mutually perpendicular |
| Phase | E and B oscillate in phase |
| Amplitude | E₀ = cB₀ |
| Speed in vacuum | c = 3x10^8 m/s |
| Propagation | No medium required |
| Deflection | Not deflected by E or B fields |
| Phenomena | Reflection, refraction, diffraction, polarization |
The Electromagnetic Spectrum
| Type | Wavelength | Frequency | Applications |
|---|---|---|---|
| Radio waves | >0.1 m | <3 GHz | Radio, TV, mobile |
| Microwaves | 0.1 m - 1 mm | 3-300 GHz | RADAR, microwave oven, satellite |
| Infrared | 1 mm - 700 nm | 300 GHz - 430 THz | Remote controls, thermal imaging |
| Visible | 700-400 nm | 430-750 THz | Vision, photography |
| Ultraviolet | 400-1 nm | 750 THz - 3x10^17 Hz | Sterilization, LASIK |
| X-rays | 1-0.001 nm | 3x10^17-3x10^20 Hz | Medical imaging, crystallography |
| Gamma rays | <0.001 nm | >3x10^20 Hz | Cancer therapy, sterilization |
Key Applications
- Microwaves: RADAR detects aircraft; microwave oven heats food at 2.45 GHz
- Infrared: Night-vision cameras; TV remote controls (940 nm IR LED)
- UV: Kills bacteria (germicidal lamps); LASIK surgery; water purification
- X-rays: Discovered by Rontgen 1895; bone imaging; Bragg diffraction for crystal structure
- Gamma rays: Emitted by radioactive nuclei; cancer radiotherapy; PET scans
Important Note
All EM waves travel at c = 3x10^8 m/s in vacuum regardless of frequency.
EM Spectrum and Applications
The Electromagnetic Spectrum
All EM waves travel at c = 3×10⁸ m/s in vacuum but differ in frequency and wavelength.
| Type | Wavelength Range | Frequency Range | Source | Applications |
|---|---|---|---|---|
| Radio waves | > 0.1 m | < 3×10⁹ Hz | Oscillating circuits, antennas | AM/FM radio, TV, mobile |
| Microwaves | 1mm – 0.1m | 3×10⁹ – 3×10¹¹ Hz | Klystron, magnetron | RADAR, microwave oven, WiFi |
| Infrared (IR) | 700nm – 1mm | 3×10¹¹ – 4×10¹⁴ Hz | Hot bodies, IR LEDs | Remote controls, night vision, heaters |
| Visible light | 400–700 nm | 4–7.5×10¹⁴ Hz | Hot objects, atoms | Vision, photography, lighting |
| Ultraviolet (UV) | 1–400 nm | 7.5×10¹⁴ – 3×10¹⁷ Hz | Sun, hot stars, UV lamps | Sterilization, Vitamin D, fluorescence |
| X-rays | 0.001–10 nm | 3×10¹⁶ – 3×10¹⁹ Hz | Bombarding metals with electrons | Medical imaging, crystallography |
| Gamma rays | < 0.001 nm | > 3×10¹⁹ Hz | Radioactive nuclei | Cancer treatment, sterilization |
Key Points on EM Spectrum
Increasing wavelength: Gamma → X-ray → UV → Visible → IR → Microwave → Radio Increasing frequency and energy: Radio → Microwave → IR → Visible → UV → X-ray → Gamma
Energy of photon: E = hf = hc/λ, where h = 6.63×10⁻³⁴ J·s (Planck's constant)
Greenhouse Effect
- Sunlight (visible + UV) passes through atmosphere → absorbed by Earth
- Earth emits IR radiation → trapped by CO₂, CH₄, H₂O vapor
- Temperature rises → global warming
Important Applications
- RADAR: Microwaves reflected from objects → detects position and speed
- MRI: Radio waves resonate with nuclei in magnetic field → medical imaging
- Astronomy: Optical, radio, X-ray, gamma-ray telescopes
- Optical fiber: Total internal reflection of IR light
- Remote sensing: IR and microwave from satellites
Ozone Layer
The ozone (O₃) layer in the stratosphere absorbs most of the UV radiation from the Sun.
- UV causes skin cancer, cataracts, and damages ecosystems
- CFCs deplete ozone layer → increased UV reaching Earth
- UV-C (most harmful, λ < 280 nm) completely blocked by ozone
Diagram Indicator: [Linear EM spectrum diagram with all 7 types arranged by wavelength from gamma (shortest) to radio (longest); arrows showing increasing frequency left to right and increasing wavelength right to left; visible spectrum VIBGYOR shown in middle.]
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Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Electromagnetic Waves.