Fields (Units 4 and 5) unifies gravity, electricity, and magnetism — inverse-square laws, field lines, potentials, capacitance, and electromagnetic induction lead to understanding of modern physics.
Gravitational field strength g = F/m (N/kg). Newton\'s law of gravitation: F = Gm₁m₂/r². Radial field: g = GM/r². Gravitational potential V_g = −GM/r (J/kg, negative because attractive). Escape velocity v = √(2GM/r). Orbits: gravitational force = centripetal force → v = √(GM/r), T² ∝ r³. Geostationary: T = 24h, equatorial, same direction as rotation. Electric field E = F/Q (N/C). Coulomb\'s law: F = kQ₁Q₂/r². Uniform field between parallel plates: E = V/d. Electric potential V_e = kQ/r.
Capacitance C = Q/V (F). Energy stored = ½QV = ½CV² = ½Q²/C. Parallel plate: C = εA/d. Charge/discharge: exponential Q = Q₀e^(−t/RC). Time constant τ = RC. Graphs: charge on capacitor vs time (exponential decay for discharge). Magnetic flux density B (T). Force on wire: F = BIL sinθ. Force on moving charge: F = BQv sinθ (basis of particle accelerators). Magnetic flux Φ = BA cosθ (Wb). Faraday\'s law: induced emf = −NΔΦ/Δt. Lenz\'s law: induced current opposes the change. Applications: generators, transformers. Transformer: V₁/V₂ = N₁/N₂.
Gravitational potential V_g at a point is defined as the work done per unit mass in bringing a small test mass from infinity to that point. At infinity, V_g = 0 by definition. Since gravity is always attractive, a mass naturally falls inward — so you don\'t need to do work to bring it in; gravity does the work. This means the mass loses potential energy as it approaches, making V_g negative. The closer to the mass (source), the more negative V_g becomes: V_g = −GM/r. To escape from a gravitational field (move to infinity), you must add energy — this is why escape velocity exists. The negative sign is a consequence of choosing infinity as the zero reference point and gravity being purely attractive (unlike electric fields which can be attractive or repulsive).
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