Electricity and Magnetism
Core concepts
Electrostatics: Coulomb's law, electric field, electric potential and potential energy, Gauss's law conceptually, capacitors and dielectrics. Circuits: Ohm's law, series and parallel combinations, Kirchhoff's rules, power dissipation, internal resistance. Magnetism: magnetic force on moving charges and current-carrying wires, fields of wires and solenoids, electromagnetic induction (Faraday and Lenz), and simple AC/transformer relations.
Traps to watch
- Field vs. potential: field is a vector (force per charge); potential is a scalar (energy per charge). Field points from high to low potential.
- Series vs. parallel: series shares current and adds resistance; parallel shares voltage and adds conductance (1/R_total = sum of 1/R).
- Capacitors in circuits: in parallel they add capacitance; in series they combine reciprocally - the opposite of resistors.
- Lenz's law: induced current opposes the change in flux, not the flux itself. Direction questions hinge on this wording.
- Magnetic force does no work on a moving charge because it is perpendicular to velocity.
- Power formulas: P = IV = I²R = V²/R; pick the form matching the quantities held constant.
Rule of thumb
For multi-resistor networks, reduce series and parallel groups stepwise to a single equivalent resistance, find total current from the source, then work back outward for branch currents and voltage drops.
Worked example
Two 6 Ω resistors in parallel, in series with a 3 Ω resistor, across a 12 V source. Parallel pair: 1/R = 1/6 + 1/6 = 1/3, so R_p = 3 Ω. Total R = 3 + 3 = 6 Ω. Total current = 12/6 = 2 A. Voltage across the parallel pair = 2 × 3 = 6 V, so each 6 Ω branch carries 1 A.