Fields, Electromagnetism and Induction
Gravitational and electric fields
Gravitational field strength g = F/m; near a point mass g = GM/r². Electric field strength E = F/q; for a point charge E = Q/(4πε₀r²). Field lines show direction; uniform fields have parallel, equally spaced lines. Work done moving a charge through a potential difference is W = QV.
Magnetic forces and induction
A current-carrying wire in a magnetic field experiences F = BIL sin θ. A moving charge experiences F = Bqv sin θ. Magnetic flux Φ = BA cos θ, where θ is between the field and the normal to the area. Faraday’s law: induced EMF = −N ΔΦ/Δt. Lenz’s law gives the minus sign: the induced current opposes the change producing it. Transformers use mutual induction; for an ideal transformer, Vp/Vs = Np/Ns and input power equals output power.
Worked example
A 200-turn coil of area 0.020 m² is in a magnetic field that changes from 0.10 T to 0.50 T in 0.20 s. Change in flux density = 0.40 T, so ΔΦ per turn = 0.40 × 0.020 = 8.0 × 10⁻³ Wb. Induced EMF = N ΔΦ/Δt = 200 × 8.0 × 10⁻³ ÷ 0.20 = 8.0 V. The direction of the induced current would oppose the increase in flux.
Traps
Confusing magnetic flux with flux density; using the angle between field and plane instead of field and normal; dropping the negative sign of Lenz’s law; assuming an EMF is induced when flux is constant; applying transformer equations to a non-ideal transformer without allowing for losses.