Class 12 Physics Notes Chapter 8 (Electromagnetic waves) – Physics Part-I Book

Detailed Notes with MCQs of Chapter 8: Electromagnetic Waves. This is a relatively short but conceptually important chapter, especially for objective questions in competitive exams. It bridges the gap between electricity/magnetism and optics.

Chapter 8: Electromagnetic Waves - Detailed Notes for Government Exam Preparation

1. Introduction & Need for Displacement Current:

• Inconsistency of Ampere's Circuital Law: James Clerk Maxwell observed that Ampere's Circuital Law (∮ B ⋅ dl = μ₀I_enc) was logically inconsistent when applied to situations involving time-varying electric fields, such as the charging or discharging of a capacitor.
• Example: Charging Capacitor: Consider the space between the plates of a charging capacitor. There is no conduction current (I = 0) flowing between the plates. However, experiments show a magnetic field exists around this region. Ampere's law in its original form couldn't explain this.
• Maxwell's Postulate: Maxwell proposed that a changing electric field (or electric flux) in a region of space produces a magnetic field, just like a conduction current does.
• Displacement Current (I_d): This is the current equivalent associated with a changing electric flux. It's not a flow of charge.
  • Definition: I_d = ε₀ (dΦ_E / dt)
    • where ε₀ is the permittivity of free space, and Φ_E is the electric flux (Φ_E = ∫ E ⋅ dA).
  • Significance: It ensures the continuity of current in circuits (e.g., Conduction current flows to the capacitor plate, and an equivalent displacement current exists between the plates).

2. Ampere-Maxwell Law (Modified Ampere's Law):

• Maxwell modified Ampere's law to include the displacement current.
• Integral Form: ∮ B ⋅ dl = μ₀ (I_c + I_d) = μ₀ (I_c + ε₀ dΦ_E / dt)
  • where I_c is the conduction current (due to charge flow) and I_d is the displacement current (due to changing electric flux).
• Key Point: This law implies that magnetic fields are produced not only by conduction currents but also by time-varying electric fields.

3. Maxwell's Equations (Conceptual Summary):

Maxwell unified the laws of electricity and magnetism into four fundamental equations:

1. Gauss's Law for Electrostatics: ∮ E ⋅ dA = Q_enc / ε₀ (Relates electric field to charge distribution).
2. Gauss's Law for Magnetism: ∮ B ⋅ dA = 0 (Implies magnetic monopoles do not exist; magnetic field lines are closed loops).
3. Faraday's Law of Induction: ∮ E ⋅ dl = - dΦ_B / dt (A changing magnetic flux induces an electric field - EMF).
4. Ampere-Maxwell Law: ∮ B ⋅ dl = μ₀ I_c + μ₀ ε₀ dΦ_E / dt (Magnetic fields are produced by conduction currents and/or changing electric fields).

Significance: These equations form the foundation of classical electromagnetism and predict the existence of electromagnetic waves.

4. Electromagnetic Waves (EM Waves):

• Prediction: Maxwell's equations showed that time-varying electric and magnetic fields can propagate through space as waves, mutually sustaining each other.
• Source: The fundamental cause of EM waves is an accelerated electric charge. An oscillating charge (like in an LC circuit or antenna) is a common source. Stationary charges produce only electric fields, and charges moving with constant velocity produce both electric and magnetic fields (but not EM waves).
• Nature:
  • Transverse: The electric field (E) and magnetic field (B) vectors are perpendicular to each other and also perpendicular to the direction of wave propagation (k or v). The direction of propagation is given by the direction of E × B.
  • Self-Sustaining: Changing B produces E (Faraday's Law), and changing E produces B (Ampere-Maxwell Law).
  • Medium Not Required: EM waves can travel through a vacuum.
  • Speed:
    • In vacuum: c = 1 / √(μ₀ε₀) ≈ 3 × 10⁸ m/s (Speed of light). This value derived from electromagnetic constants (μ₀, ε₀) matched the measured speed of light, strongly suggesting light is an EM wave.
    • In a material medium: v = 1 / √(με) = c / √(μ_rε_r) = c / n
      • μ = permeability of the medium (μ = μ₀μ_r)
      • ε = permittivity of the medium (ε = ε₀ε_r)
      • n = √(μ_rε_r) is the refractive index of the medium.
  • Phase: The E and B fields oscillate in phase with each other.
  • Relation between E and B magnitudes: In vacuum, E₀ / B₀ = c, or E / B = c (where E₀, B₀ are amplitudes and E, B are instantaneous values). In a medium, E / B = v.
  • Wave Properties: EM waves exhibit reflection, refraction, interference, diffraction, and polarization (Polarization confirms the transverse nature).

5. Energy and Momentum of EM Waves:

• Energy Density: EM waves transport energy. The energy is stored in the electric and magnetic fields.
  • Energy density due to electric field: u_E = ½ ε₀ E²
  • Energy density due to magnetic field: u_B = B² / (2μ₀)
  • Important Relation: In an EM wave (in vacuum or medium), the energy density of the electric field equals the energy density of the magnetic field: u_E = u_B.
  • Total instantaneous energy density: u = u_E + u_B = ε₀ E² = B² / μ₀
  • Average energy density: u_avg = ½ ε₀ E₀² = B₀² / (2μ₀) = ε₀ E_rms² = B_rms² / μ₀
• Intensity (I): The average energy crossing per unit area per unit time, perpendicular to the direction of propagation. Also known as the magnitude of the average Poynting vector (S_avg).
  • I = S_avg = u_avg * c = (½ ε₀ E₀²) c = [B₀² / (2μ₀)] c
• Poynting Vector (S): Represents the directional energy flux density (Energy per unit time per unit area) of an EM wave. S = (1/μ₀) (E × B). Its direction gives the direction of energy flow.
• Momentum: EM waves carry linear momentum.
  • If energy U is completely absorbed by a surface: Momentum transferred p = U / c.
  • If energy U is completely reflected by a surface: Momentum transferred p = 2U / c.
• Radiation Pressure: The pressure exerted by EM waves on a surface.
  • For complete absorption: Pressure = Intensity / c = I / c.
  • For complete reflection: Pressure = 2 * Intensity / c = 2I / c.

6. Electromagnetic Spectrum:

• The classification of EM waves according to their frequency (or wavelength) is called the electromagnetic spectrum. There are no sharp boundaries between different types.

• Order (Increasing Frequency / Decreasing Wavelength):

  • Radio waves: > 0.1 m wavelength. Produced by oscillating circuits (LC oscillators), antennas. Used in radio/TV broadcasting, radar, navigation.
  • Microwaves: 0.1 m to 1 mm wavelength. Produced by special vacuum tubes (klystrons, magnetrons). Used in radar, microwave ovens, telecommunications (mobile phones, Wi-Fi).
  • Infrared (IR) waves: 1 mm to 700 nm wavelength. Produced by hot bodies, molecular vibrations. Used in remote controls, thermal imaging (night vision), physiotherapy, greenhouse effect. Detected by thermopiles, bolometers.
  • Visible Light: 700 nm (Red) to 400 nm (Violet) wavelength. Produced by excitation of atoms (e.g., lamps, Sun). Detected by eyes, photographic film, photocells. The familiar VIBGYOR spectrum.
  • Ultraviolet (UV) waves: 400 nm to 1 nm wavelength. Produced by the Sun, special lamps, very hot bodies, electric arcs. Used in detecting forged documents, sterilizing medical instruments (germicidal lamps), water purifiers, vitamin D production. Can cause skin tan/cancer. Absorbed by ozone layer.
  • X-rays: 1 nm to 10⁻³ nm wavelength. Produced by bombarding a metal target with high-energy electrons (X-ray tubes), inner shell electron transitions. Used in medical imaging (detecting fractures), cancer treatment, studying crystal structures, security scanners.
  • Gamma (γ) rays: < 10⁻³ nm wavelength. Produced in nuclear reactions (radioactive decay), particle accelerators, cosmic rays. Highly penetrating. Used in radiotherapy (cancer treatment), sterilizing food and medical equipment, detecting flaws in castings.

• Key Trend: As frequency increases (ν ↑), wavelength decreases (λ ↓), energy per photon increases (E = hν ↑), and penetrating power generally increases.

Multiple Choice Questions (MCQs):

1. The concept of displacement current was introduced by:
   (a) Ampere
   (b) Faraday
   (c) Maxwell
   (d) Hertz

2. Which of the following is the primary source of electromagnetic waves?
   (a) A stationary charge
   (b) A charge moving with constant velocity
   (c) An accelerated charge
   (d) A charge-less particle

3. In an electromagnetic wave propagating in vacuum, the electric field (E) and magnetic field (B) are:
   (a) Parallel to each other and perpendicular to the direction of propagation.
   (b) Perpendicular to each other and parallel to the direction of propagation.
   (c) Perpendicular to each other and perpendicular to the direction of propagation.
   (d) Parallel to each other and parallel to the direction of propagation.

4. The speed of electromagnetic waves in a material medium with relative permittivity ε_r and relative permeability μ_r is given by:
   (a) c / √(μ_rε_r)
   (b) c √(μ_rε_r)
   (c) c / (μ_rε_r)
   (d) c

5. If E₀ and B₀ are the amplitudes of the electric and magnetic fields respectively in an electromagnetic wave in vacuum, then:
   (a) E₀ B₀ = c
   (b) E₀ / B₀ = c
   (c) B₀ / E₀ = c
   (d) E₀ B₀ = 1/c

6. Which part of the electromagnetic spectrum is used in radar systems?
   (a) Infrared waves
   (b) Ultraviolet waves
   (c) Microwaves
   (d) X-rays

7. Arrange the following electromagnetic waves in increasing order of their frequencies: I. Microwaves, II. Gamma rays, III. Radio waves, IV. X-rays
   (a) III, I, IV, II
   (b) III, I, II, IV
   (c) I, III, IV, II
   (d) II, IV, I, III

8. The energy density of the electric field (u_E) and magnetic field (u_B) in an electromagnetic wave in vacuum are related as:
   (a) u_E > u_B
   (b) u_E < u_B
   (c) u_E = u_B
   (d) u_E = 1/u_B

9. Which phenomenon demonstrates the transverse nature of electromagnetic waves?
   (a) Reflection
   (b) Refraction
   (c) Interference
   (d) Polarization

10. An electromagnetic wave transfers energy U to a perfectly reflecting surface. The momentum transferred to the surface is:
    (a) U/c
    (b) 2U/c
    (c) U*c
    (d) U/(2c)

Answer Key:

1. (c)
2. (c)
3. (c)
4. (a)
5. (b)
6. (c)
7. (a)
8. (c)
9. (d)
10. (b)

Make sure you understand the concepts behind these points and the applications of different parts of the EM spectrum. Good luck with your preparation!