Fields: Gravitational, Electric and Magnetic Fields, and Electromagnetic Induction
Gravitational and electric fields
Field strength is force per unit mass or charge: g = GM/r² and E = kQ/r². Potential is energy per unit mass or charge: V_g = −GM/r and V_e = kQ/r. Equipotentials are perpendicular to field lines. In a uniform field, E = V/d, and the force on a charge is QE.
Magnetic fields
Magnetic flux density B is force per unit current per unit length: F = BIL sinθ. A moving charge feels F = Bqv sinθ; if v is perpendicular to B, it moves in a circle of radius r = mv/(qB). The force is always perpendicular to velocity, so magnetic fields do no work on the charge.
Electromagnetic induction
Magnetic flux Φ = BA cosθ; flux linkage = NΦ. Faraday's law gives induced EMF ε = −d(NΦ)/dt. Lenz's law says the induced current opposes the change producing it, a consequence of energy conservation.
Worked example
A 200-turn coil of area 0.010 m² lies perpendicular to a field that rises from 0.20 T to 0.60 T in 0.50 s. ε = N A ΔB/Δt = 200 × 0.010 × 0.40/0.50 = 1.6 V. With a 4.0 Ω circuit, the induced current is 0.40 A. The current direction creates a field opposing the increase.
Traps
Confusing flux with flux linkage; forgetting the cosθ factor when the coil is not perpendicular; dropping the minus sign in Lenz's law; using g = GM/r instead of GM/r²; treating potential as a vector.