Electricity and Magnetism
Core concepts
Electric fields describe the force per unit positive charge, E = F/q, and around a point charge E = kQ/r². Electric potential is energy per unit charge, and potential difference drives current. Uniform fields between parallel plates give E = V/d, useful for charged-particle motion problems.
Circuits require Ohm's law V = IR, power P = VI = I²R = V²/R, and the rules for series and parallel networks. In series, current is common and voltages add; in parallel, voltage is common and currents add. Kirchhoff's laws formalise conservation of charge and energy. Internal resistance means terminal voltage falls as current rises: V_terminal = emf − Ir.
Magnetic fields exert forces on moving charges (F = qvB sinθ) and on current-carrying wires (F = BIL sinθ), with direction given by the right-hand rule. A charge moving parallel to a field feels no force. Magnetic flux Φ = BA cosθ and Faraday's law (induced emf proportional to rate of change of flux) underpin generators and transformers. Lenz's law states the induced current opposes the change producing it.
Traps
Confusing field strength with potential; forgetting sinθ in magnetic force; assuming a charge always experiences a magnetic force; ignoring internal resistance; mixing series and parallel rules; forgetting that flux depends on the angle between field and area normal.
Worked example
A 12 V battery with 0.5 Ω internal resistance drives a 5.5 Ω resistor. Total resistance is 6.0 Ω, so I = 12/6.0 = 2.0 A. Terminal voltage is 12 − (2.0)(0.5) = 11 V. Rule of thumb: always add internal resistance to the external circuit before applying Ohm's law to the whole loop.