Electricity and Magnetism
Electricity and Magnetism tests Coulomb’s law, electric field and potential, DC circuits, Kirchhoff’s rules, magnetic force, and electromagnetic induction. Numerical sign discipline matters as much as formulas.
Core rules
- Coulomb: F = kq₁q₂/r²; field E = F/q; potential V = kq/r (scalar).
- Series: same current, R_total = ΣR. Parallel: same voltage, 1/R_total = Σ1/R.
- Kirchhoff: junction currents sum to zero; loop voltage changes sum to zero.
- Magnetic force on a wire: F = BIL sinθ; direction from Fleming’s left-hand rule.
- Induced emf: ε = −dΦ/dt; Lenz’s law opposes the change in flux.
Worked example
A 12 V battery of negligible internal resistance is connected to 6 Ω and 3 Ω resistors in parallel. Find the total current and each branch current. Parallel resistance: 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, so R = 2 Ω. Total current: I = V/R = 12/2 = 6 A. Each branch has the full 12 V: I_6 = 12/6 = 2 A; I_3 = 12/3 = 4 A. Check: 2 A + 4 A = 6 A, matching the total. The smaller resistor carries the larger current.
Traps
- Adding parallel resistances directly instead of using reciprocals.
- Assuming current is used up around a series circuit.
- Ignoring internal resistance, which reduces terminal voltage under load.
- Reversing the magnetic-force direction for a negative charge.
- Treating electric potential as a vector; it is a scalar.