Electricity and Magnetism
Electricity and Magnetism tests electrostatic force and field, potential, capacitance, DC circuits, magnetic force and electromagnetic induction. You should be able to select the correct law and to track charge, current, energy and flux through a circuit or coil.
Core rules
- Coulomb’s law: F = kq₁q₂/r², with k ≈ 8.99 × 10⁹ N m² C⁻². Electric field E = F/q; potential V = W/q.
- In series, resistances add; in parallel, 1/R_total = 1/R₁ + 1/R₂ + … . Ohm’s law is V = IR; power is P = VI = I²R.
- A capacitor stores charge Q = CV and energy ½CV². It blocks steady direct current once charged.
- Magnetic force on a current is F = BIL sin θ; on a moving charge it is F = qvB sin θ.
- Magnetic flux is Φ = BA cos θ, where θ is the angle between the field and the normal to the area. Faraday’s law gives induced emf magnitude N ΔΦ/Δt; Lenz’s law gives the direction opposing the change.
Worked example
A coil of 200 turns and area 0.020 m² is in a field that falls from 0.50 T to 0 in 0.10 s. The flux change per turn is BA = 0.50 × 0.020 = 0.010 Wb. The induced emf magnitude is N ΔΦ/Δt = 200 × 0.010 / 0.10 = 20 V. By Lenz’s law, the induced current opposes the decrease in flux, so its magnetic field is in the same direction as the original field.
Traps
Convert μC to C before Coulomb’s law. Do not add parallel resistances directly. Flux depends on the perpendicular area, so use cos θ. Induced emf depends on the rate of change of flux, not on the flux itself. Lenz’s law gives direction, not magnitude.