NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves
NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves offers short notes, key mathematical relations, displacement current concept, Maxwell's equations, speed of EM waves, and complete classification of the electromagnetic spectrum with practical applications.
Overview of Topics & Subtopics (Click to Jump)
1. Displacement Current & Maxwell's Equations
Short Note:
• Need for Displacement Current: Ampere's Circuital Law was found to be logically inconsistent for time-varying electric fields (such as charging a capacitor). Maxwell modified the law by adding displacement current.
• Displacement Current (I_d): Current arising due to time-varying electric field / electric flux: I_d = ε₀ (dΦ_E / dt).
• Ampere-Maxwell Law: Total current = Conduction current (I_c) + Displacement current (I_d). ∮ B · dl = μ₀ (I_c + ε₀ dΦ_E / dt).
• Maxwell's Four Fundamental Equations:
1. Gauss's Law in Electrostatics: ∮ E · dA = q / ε₀
2. Gauss's Law in Magnetism: ∮ B · dA = 0
3. Faraday's Law of Electromagnetic Induction: ∮ E · dl = -dΦ_B / dt
4. Ampere-Maxwell Law: ∮ B · dl = μ₀ I_c + μ₀ ε₀ (dΦ_E / dt)
2. Electromagnetic Waves & Their Characteristics
Short Note:
• Nature of EM Waves: Coupled sinusoidal electric and magnetic field vectors oscillating mutually perpendicular to each other and perpendicular to direction of propagation (Transverse Nature).
• Speed of EM Waves:
- In Vacuum: c = 1 / √(μ₀ ε₀) ≈ 3 × 10⁸ m/s.
- In Material Medium: v = 1 / √(μ ε) = c / n, where n is refractive index.
• Ratio of Amplitudes: Amplitude ratio of electric field E₀ to magnetic field B₀ equals speed of light: c = E₀ / B₀ = E_rms / B_rms.
• Energy Density: Energy is shared equally between electric and magnetic fields:
- Average Energy Density: u = u_E + u_B = (1/2) ε₀ E_rms² + (1 / 2μ₀) B_rms² = ε₀ E_rms².
• Momentum & Radiation Pressure: EM wave transports linear momentum p = U / c (where U is energy). When absorbed by surface, it exerts pressure called Radiation Pressure.
3. Electromagnetic Spectrum & Its Applications
Short Note:
Classification of EM waves in order of increasing frequency (decreasing wavelength):
1. Radio Waves (λ > 0.1 m): Produced by accelerated motion of charges in conducting wires. Used in radio & TV broadcasting.
2. Microwaves (0.1 m to 1 mm): Produced by special vacuum tubes (klystrons, magnetrons). Used in radar systems and microwave ovens.
3. Infrared Waves (1 mm to 700 nm): Heat waves produced by hot bodies and molecules. Used in remote controls, night-vision devices, and greenhouse effect.
4. Visible Light (700 nm to 400 nm): Emitted by atomic excitation. Provides vision to human eyes.
5. Ultraviolet Rays (400 nm to 1 nm): Produced by high-voltage lamps and Sun. Used in water purifiers, sterilization, and LASIK eye surgery.
6. X-Rays (1 nm to 10⁻³ nm): Produced by bombarding metal target with high-energy electrons. Used in medical diagnosis and structure detection.
7. Gamma Rays (< 10⁻³ nm): Emitted by radioactive nuclei during nuclear transitions. Used in cancer radiotherapy.
Intext & Conceptual Questions
• Ampere's Circuital Law states ∮ B · dl = μ₀ I_c. During the charging of a capacitor, a conduction current flows in the wires, but no actual charge moves across the space between the capacitor plates. Applying Ampere's law to a flat surface yields a non-zero magnetic field, whereas applying it to a bulging surface passing between plates yields zero, causing a contradiction.
• Maxwell introduced the concept of displacement current (I_d = ε₀ dΦ_E / dt) arising from the changing electric flux between capacitor plates.
• Between the plates, I_c = 0 and I_d = I, while outside in wires, I_c = I and I_d = 0. Hence, total current I_total = I_c + I_d remains continuous throughout the circuit.
| Type of Wave | Wavelength Range | Frequency Range | Primary Application |
|---|---|---|---|
| Radio Waves | > 0.1 m | < 3 × 10⁹ Hz | Radio and television communication. |
| Microwaves | 0.1 m – 1 mm | 3 × 10⁹ Hz – 3 × 10¹¹ Hz | Radar systems, satellite communication & ovens. |
| Infrared | 1 mm – 700 nm | 3 × 10¹¹ Hz – 4 × 10¹⁴ Hz | Night vision, remote controls & heat lamps. |
| Visible Light | 700 nm – 400 nm | 4 × 10¹⁴ Hz – 7.5 × 10¹⁴ Hz | Optical vision, photography. |
| Ultraviolet | 400 nm – 1 nm | 7.5 × 10¹⁴ Hz – 3 × 10¹⁶ Hz | Water purification, sterilization, LASIK. |
| X-Rays | 1 nm – 10⁻³ nm | 3 × 10¹⁶ Hz – 3 × 10¹⁹ Hz | Medical radiography, bone fracture detection. |
| Gamma Rays | < 10⁻³ nm | > 3 × 10¹⁹ Hz | Cancer radiotherapy and nuclear studies. |
Textbook Chapter End Exercise Questions
Given:
• Radius of circular plates (R_p) = 1.0 m
• Distance from center (r) = 0.5 m (halfway)
• Capacitance (C) = 1 nF = 10⁻⁹ F
• Resistance (R) = 1 MΩ = 10⁶ Ω => Time constant (τ = R C) = 10⁶ × 10⁻⁹ = 10⁻³ s
• Voltage (V₀) = 2 V, Time (t) = 10⁻³ s = τ
Step 1: Charging Current formula
I(t) = (V₀ / R) × e^(-t / τ)
At t = τ:
I = (2 / 10⁶) × e⁻¹ = 2 × 10⁻⁶ × 0.368 = 0.736 × 10⁻⁶ A
Step 2: Magnetic Field inside capacitor at distance r
Using Ampere-Maxwell law inside circular plates:
B = (μ₀ r I_d) / (2π R_p²) = (4π × 10⁻⁷ × 0.5 × 0.736 × 10⁻⁶) / (2π × 1.0²)
B = 2 × 10⁻⁷ × 0.5 × 0.736 × 10⁻⁶ = 0.736 × 10⁻¹³ T
The magnetic field at point P at t = 10⁻³ s is 0.736 × 10⁻¹³ T.
Given:
• Frequency (f) = 2.0 × 10¹⁰ Hz
• Electric field amplitude (E₀) = 48 V/m
• Speed of light in vacuum (c) = 3.0 × 10⁸ m/s
Part (a): Wavelength (λ)
λ = c / f = (3.0 × 10⁸) / (2.0 × 10¹⁰) = 1.5 × 10⁻² m = 1.5 cm
Part (b): Amplitude of Magnetic Field (B₀)
B₀ = E₀ / c = 48 / (3.0 × 10⁸) = 1.6 × 10⁻⁷ T
• The wavelength of the wave is 1.5 cm (or 1.5 × 10⁻² m).
• The amplitude of the oscillating magnetic field is 1.6 × 10⁻⁷ T.
Read More & Chapter Resources
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