Electricity and Magnetism
Electricity and Magnetism
This domain tests electrostatics, circuits, magnetism, and induction. Items range from Coulomb's law and electric potential to series and parallel networks and Faraday's law, so track both magnitude and direction.
Core rules
- Coulomb's law: F = k|q₁q₂|/r², with k ≈ 8.99 × 10⁹ N·m²/C². Electric field E = F/q and, for a point charge, E = kq/r²; field lines point away from positive charge.
- Electric potential V = kq/r; potential difference is work per unit charge. Equipotential lines are perpendicular to electric field lines.
- Ohm's law V = IR. In series, current is the same and R_eq = R₁ + R₂ + …; in parallel, voltage is the same and 1/R_eq = 1/R₁ + 1/R₂ + … . Kirchhoff's junction and loop rules follow from charge and energy conservation.
- Magnetic force on a moving charge is F = qvB sinθ and on a current-carrying wire is F = ILB sinθ; use the right-hand rule for direction.
- Faraday's law: induced emf = −NΔΦ/Δt. Lenz's law says the induced current opposes the change in flux.
Worked example
A 12 V battery connects to a 6 Ω and a 3 Ω resistor in parallel. The equivalent resistance is 1/R_eq = 1/6 + 1/3 = 1/2, so R_eq = 2 Ω. Total current is I = 12/2 = 6 A. The 6 Ω branch carries 12/6 = 2 A and the 3 Ω branch carries 12/3 = 4 A; the branch currents add to 6 A. Each resistor dissipates P = V²/R: 24 W and 48 W.
Traps
- Adding parallel resistances directly, which underestimates R_eq.
- Forgetting that ideal voltmeters have very high resistance and ammeters very low resistance.
- Reversing Lenz's law: induced current opposes the flux change, not the flux itself.
- Using degrees instead of the angle between v and B in F = qvB sinθ.