Electricity and Magnetism
The Electricity and Magnetism domain tests Coulomb's law, electric field and potential, direct-current circuits, magnetic forces, and electromagnetic induction. Circuit questions reward careful bookkeeping: what is shared, what splits, and what is conserved.
Electrostatics
Coulomb's law: F = kq₁q₂/r², with k ≈ 8.99 × 10⁹ N·m²/C². Electric field E = F/q; for a point charge E = kq/r². Potential V = kq/r, and potential energy for a charge in a potential is U = qV. Field lines point from positive to negative and are perpendicular to conductors.
Circuits
Ohm's law: V = IR. Power: P = IV = I²R = V²/R. In series, current is the same and resistances add. In parallel, voltage is the same and 1/R_eq = 1/R₁ + 1/R₂ + … Kirchhoff's junction rule conserves charge; the loop rule conserves energy.
Magnetism
A moving charge feels F = qvB sinθ; a current-carrying wire feels F = BIL sinθ. The force is perpendicular to both v and B, so it does no work. A current produces a magnetic field; a changing magnetic flux induces an emf, ε = −N ΔΦ/Δt, and Lenz's law says the induced current opposes the change in flux.
Worked example
A 12 V battery connects across a 4.0 Ω and a 6.0 Ω resistor in parallel. Find the total current and each branch current. 1/R_eq = 1/4.0 + 1/6.0 = 0.250 + 0.167 = 0.417 Ω⁻¹, so R_eq = 2.4 Ω. I_total = 12/2.4 = 5.0 A. Each branch has the full 12 V: I₄ = 12/4.0 = 3.0 A and I₆ = 12/6.0 = 2.0 A; they sum to 5.0 A.
Traps
- Adding parallel resistances directly.
- Thinking current is used up as it passes through resistors.
- Forgetting to convert centimeters to meters in Coulomb's law.
- Using the angle between v and B incorrectly; F = 0 when they are parallel.
- Reversing Lenz's law so the induced current aids the change.