Section 1: Displacement Current and the Modified Ampere Law

The chapter begins with Maxwell's resolution of an inconsistency in Ampere's law for a charging capacitor. In the external wire, conduction current I_c flows. Between the capacitor plates, no charge flows, but the electric field (and hence electric flux Φ_E) increases as the capacitor charges. Maxwell introduced displacement current Id = ε_{0}(dΦ_E/dt), which: (a) is not actual charge flow; (b) equals the conduction current in the external wire; (c) produces a magnetic field identically to how a real current does. The modified Ampere-Maxwell law ∮B·dl = μ_{0}(I_c + ε_{0} dΦ_E/dt) resolves the inconsistency by ensuring equal total currents through any surface bounded by the same Amperian loop.

Numerical application: If capacitor plate area A = 0.1 $m^{2}$ and dE/dt = $5 \times 10^{12}$ V/(m·s), then Id = ε_{0} × A × (dE/dt) = ($8.85 \times 10^{-}$^{12})(0.1)($5 \times 10^{12}$) = 4.425 A.

Section 2: Maxwell's Four Equations

Maxwell unified four fundamental laws into a complete description of electromagnetism. Equation 1 (Gauss, electricity): charges produce electric fields; net E flux through closed surface = q_enc/ε_{0}. Equation 2 (Gauss, magnetism): no magnetic monopoles exist; net B flux through any closed surface = 0; B field lines are always closed loops. Equation 3 (Faraday): a time-varying B field induces an E field (∮E·dl = –dΦ_B/dt); basis of generators and transformers. Equation 4 (Ampere-Maxwell): conduction current AND displacement current produce B fields. The symmetry between equations 3 and 4 — changing B → E and changing E → B — enables self-sustaining EM wave propagation.

Section 3: Properties of Electromagnetic Waves

EM waves are produced by accelerating charges. Key properties: (1) Transverse — E ⊥ B ⊥ propagation direction; (2) In-phase — E and B oscillate with simultaneous peaks and zeros; (3) Universal speed — c = 1/√(μ_{0}ε_{0}) = $3 \times 10^{8}$ m/s in vacuum for ALL frequencies; (4) Amplitude ratio — $E_{0}$/$B_{0}$ = c; (5) Energy transport — intensity I = (1/2)ε_{0}c$E_{0}^{2}$ in W/$m^{2}$; (6) Momentum transport — p = U/c (absorption) or 2U/c (reflection), creating radiation pressure.

Section 4: The Electromagnetic Spectrum

Seven major bands in order of increasing frequency, with sources, detectors, and key applications:

• Radio (circuits) → Microwave (magnetron) → Infrared (hot bodies) → Visible (sun/bulbs) → UV (sun/Hg lamp) → X-rays (Coolidge tube) → Gamma (nuclear decay)
• Applications: Radio=broadcast; Microwave=RADAR/ovens; IR=night vision/physiotherapy; Visible=vision; UV=sterilisation/LASIK; X-ray=medical imaging; Gamma=cancer treatment

Critical X-ray vs gamma distinction: overlapping frequency ranges; classified by source alone.

Section 5: Key Numericals

Two solved problems: (N1) $E_{0}$ = 50 V/m → $B_{0}$ = $1.67 \times 10^{-7}$ T; I = 0.33 W/$m^{2}$. (N2) Capacitor A = 0.1 $m^{2}$, dE/dt = $5 \times 10^{12}$ V/(m·s) → Id = 4.425 A.

Section 6: NEET Exam Focus Areas

Most tested: EM spectrum application matching (every year), EM wave properties (E-B relationship, transverse nature, speed), displacement current concept (every 2–3 years), X-ray vs gamma distinction.