Electricity and Magnetism
Electricity and Magnetism
This domain tests electrostatic force and field, electric potential and capacitance, direct-current circuits, and magnetic forces and induction.
Core rules
- Coulomb's law: F = k|q₁q₂|/r², with k ≈ 8.99 × 10⁹ N·m²/C². Electric field E = F/q; for a point charge E = k|q|/r², directed away from positive charge.
- Potential: V = kq/r; ΔV = −Ed for a uniform field. Potential is scalar, so add contributions algebraically. Capacitance C = Q/ΔV; for a parallel-plate capacitor C = ε₀A/d.
- Circuits: Ohm's law V = IR. Series: same current, R_eq = ΣR. Parallel: same voltage, 1/R_eq = Σ(1/R). Power P = IV = I²R = V²/R.
- Magnetism: F = qvB sinθ on a moving charge; F = BIL sinθ on a current-carrying wire. Use the right-hand rule for v × B. A changing magnetic flux induces an emf, ε = −NΔΦ/Δt; Lenz's law says the induced current opposes the change in flux.
Worked example
A 12 V battery connects to a 6.0 Ω resistor in parallel with a 3.0 Ω resistor. Find the total current. The equivalent resistance is (6.0 × 3.0)/(6.0 + 3.0) = 2.0 Ω, so I = V/R = 12/2.0 = 6.0 A. Each branch has the full 12 V: 2.0 A through the 6.0 Ω branch and 4.0 A through the 3.0 Ω branch, summing to 6.0 A.
Traps
- Adding parallel resistances directly instead of using reciprocals.
- Assuming current is used up around a series circuit; charge is conserved.
- Mixing series and parallel voltage and current rules.
- Using the left hand or reversing the sign in the magnetic force rule.
- Treating Lenz's law as opposing the magnetic field itself rather than the change in flux.