P3: Gravitational, Electric and Magnetic Fields

Year 1 / ASYear 2 / A-Level All Boards (AQA, Edexcel, OCR, WJEC, CCEA) AQA

Newton's gravitation, Coulomb's law, electric potential, magnetic flux, Faraday's and Lenz's laws, circular orbit dynamics.

Exam Board:

📋 Key Definitions and Core Concepts

Faraday's Law: Induced emf is proportional to rate of change of magnetic flux linkage: ε = -N(dΦ/dt).

Lenz's Law: Direction of induced emf opposes the change in flux causing it.

Gravitational: F = GMm/r², V_g = -GM/r. Electric: F = q₁q₂/(4πε₀r²), V_E = q/(4πε₀r).
Charged particle in B-field: Bqv = mv²/r => orbital radius r = mv / (Bq).
Uniform E-field: E = V/d, F = qE = qV/d.

Exam-Style Question

Question:

Find the orbital radius of a geostationary satellite (T = 24 hrs, M_earth = 5.97 × 10²⁴ kg).

Model Solution & Mark Scheme:

GMm/r² = m(2π/T)² r => r³ = GMT² / (4π²).
r³ = (6.67 × 10⁻¹¹ × 5.97 × 10²⁴ × 86400²) / (4π²) = 7.54 × 10²² m³ => r = 4.22 × 10⁷ m (42,200 km).

Q1: Derive escape velocity from planet mass M, radius R.

Show Model Answer

Answer: ½mv² - GMm/R = 0 => v_esc = √(2GM/R).

Q2: A 200-turn coil of area 0.05 m² rotates in 0.4 T field at 50 Hz. Find peak emf.

Show Model Answer

Answer: ε_max = NABω = 200 × 0.4 × 0.05 × (2π × 50) = 1257 V (1.26 kV).

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