Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
Maxwell unified electricity, magnetism, and optics by predicting electromagnetic waves. This chapter has lower direct marks (~4–5) but concepts support optics and communication chapters. The EM spectrum is important for NEET biology-physics interface questions.
Key Concepts and Definitions
- Displacement Current (Id): Id = ε₀(dΦE/dt) — Maxwell's addition to Ampere's law
- EM Waves: Self-sustaining oscillations of E and B fields propagating in space
- Speed in vacuum: c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s
- Wave equation: c = fλ
Formulae
| Concept | Formula |
|---|---|
| Displacement current | Id = ε₀ dΦE/dt |
| Speed of EM wave | c = 1/√(μ₀ε₀) |
| Speed in medium | v = 1/√(με) |
| Refractive index | n = c/v = √(μr εr) |
| Energy density (E field) | uE = ε₀E²/2 |
| Energy density (B field) | uB = B²/2μ₀ |
| Intensity | I = Power/Area |
Maxwell's Equations (Qualitative)
1. Gauss's law for electricity: Electric field lines originate from charges 2. Gauss's law for magnetism: No magnetic monopoles (field lines form closed loops) 3. Faraday's law: Changing B creates E 4. Ampere-Maxwell law: Changing E (displacement current) creates B
These four equations together predict that E and B oscillations propagate as waves at speed c.
Properties of EM Waves
- Transverse waves — E, B, and direction of propagation are mutually perpendicular
- Do not require a medium
- Travel at c = 3 × 10⁸ m/s in vacuum
- E and B oscillate in phase
- Energy is equally divided between E and B fields
- Carry momentum — can exert radiation pressure
Electromagnetic Spectrum
| Type | Wavelength | Source | Uses |
|---|---|---|---|
| Gamma rays | < 0.01 nm | Nuclear reactions | Cancer treatment |
| X-rays | 0.01–10 nm | X-ray tubes | Medical imaging |
| Ultraviolet | 10–400 nm | Sun, UV lamps | Sterilisation |
| Visible light | 400–700 nm | Sun, lamps | Vision |
| Infrared | 700 nm–1 mm | Hot bodies | Remote controls, night vision |
| Microwaves | 1 mm–10 cm | Magnetron | Radar, microwave oven |
| Radio waves | > 10 cm | Oscillating circuits | Radio, TV, mobile |
Important Questions
One Mark
1. What is displacement current? 2. Who discovered electromagnetic waves experimentally? 3. What is the speed of EM waves in vacuum? 4. Name the EM waves used in cancer therapy. 5. Write the relation between μ₀, ε₀, and speed of light.
Short Answer (3 marks)
1. Explain why Maxwell modified Ampere's law by introducing displacement current. Give the expression. 2. List any five properties of electromagnetic waves. 3. Arrange the following EM waves in increasing order of wavelength: X-rays, visible light, microwaves, gamma rays.
Long Answer (5 marks)
1. Explain Maxwell's correction to Ampere's law. Using displacement current, show that EM waves exist and travel at the speed of light.
Board Exam Tips
- Memorise the EM spectrum table with wavelengths — 2-mark questions come from this directly
- Displacement current concept — always link to capacitor charging
- "EM waves are transverse" — relate to polarisation (next chapter)
Revision Checklist
- [ ] State Maxwell's equations qualitatively
- [ ] Define and derive displacement current
- [ ] State properties of EM waves
- [ ] Memorise EM spectrum with wavelengths and uses
- [ ] Derive c = 1/√(μ₀ε₀)