Chapter 29: Magnetic Fields

• Magnetic force: On a moving charge F = q v × B, on a current F = I L × B,  or  F = ILB sinθ.
• Path of a particle: In a constant magnetic field, a particle moves on a circle with r = mv/|q|B.
• Torque on a current loop: The magnetic dipole moment and torque on the loop are τ = μ × B, μ = NIA .

Chapter 30: Sources of the Magnetic Field

• Biot-Savart law: For a wire element ds, dB = (μ₀/4π) (I ds × r)/r² , where μ₀ = 4π × 10^–7 T·m/A.
• Examples: For a long straight wire, B = (μ₀/2π) I/r ; For a circular wire B = (μ₀/4π) I φ/r .
• Magnetic force between wires carrying currents: For two long straight wires F = (μ₀/2π) (I₁I₂/a) L .
• Ampère's law: For any closed loop C in space enclosing a current I_enc, ∫_C B · ds = μ₀ I_enc .
• Magnetic field of a long solenoid: The magnitude of the field is B = μ₀nI (n = N/L) .

Chapter 31: Faraday's Law

• Magnetic flux: The flux of B through a surface S is Φ_B = ∫_S B · dA .
• Faraday's law: When Φ_B changes in time, = –N dΦ_B/dt , or ∫_C E · ds = – dΦ_B/dt .
• Motional emf: The potential difference induced across a moving conductor, = –Blv .

Chapter 34: Electromagnetic Waves

• Maxwell's equations: They contain all information on how electric and magnetic fields are produced,

∫_S E · dA = q_enc/ε₀ , ∫_C E · ds = – dΦ_B/dt , ∫_S B · dA = 0 , ∫_C B · ds = μ₀I_enc + μ₀ε₀ dΦ_E/dt .

• Electromagnetic waves: Plane harmonic waves E = E_max cos(kx – ωt) and B = B_max cos(kx – ωt),
  with k = 2π/λ, ω = 2πf and, as for all waves, λf = v, the speed; E/B = c, c = (μ₀ε₀)^–1/2 = 3.00 × 10⁸ m/s .
• Energy, momentum: Poynting vector S = (1/μ₀) E × B, P = S/c or 2S/c (absorbing or reflecting surface).

Chapter 35, 36: The Nature of Light and Ray Optics, and Image Formation

• Reflection: The law of reflection, θ₁' = θ₁ .
• Refraction: Index of refraction n = c/v; The law of refraction, n₁ sin θ₁ = n₂ sin θ₂ .
• Curved mirrors: Focal length f = R/2; Mirror equation 1/p + 1/q = 1/f ; and M = h'/h = –q/p.

Chapters 37, 38: Wave Optics and Diffraction Patterns and Polarization

• Interference pattern: For two thin slits, bright fringes are located at d sin θ = mλ, with m = 0, ±1, ±2, ...
• Diffraction pattern: For a narrow slit, dark fringes are located at a sin θ = mλ, with m = ±1, ±2, ...

Chapters 39, 40: Relativity and Introduction to Quantum Physics

• Length contraction, time dilation: L = L_p/ γ, and Δt = γ Δt_p, γ = 1/(1–v²/c²)^1/2.
• Light as particles: E = hf , where h = 6.63 × 10^–34 J·s is Planck's constant; Wavelength λ = h/p.
• Uncertainty principle: Δx Δp ≥ (1/2) h/2π.