Electricity and Magnetism
Core concepts
Electrostatics: Coulomb's law gives force between point charges, F = kq₁q₂/r². Electric field E = F/q; field lines point from positive to negative. Electric potential V is scalar; potential energy U = qV. Conductors in equilibrium have zero internal field and charge resides on the surface.
Direct current: Ohm's law V = IR for ohmic conductors. For series circuits, current is common and resistances add; for parallel circuits, voltage is common and conductances add. Kirchhoff's rules (junction and loop) handle multi-loop circuits. Power dissipated is P = IV = I²R = V²/R. Internal resistance of a source reduces terminal voltage: V_terminal = ε − Ir.
Magnetic field: a current-carrying wire experiences F = BIL·sinθ; a moving charge experiences F = qvB·sinθ. Use the right-hand rule for direction. A current loop or solenoid produces a magnetic field; solenoids behave like bar magnets.
Electromagnetic induction: a changing magnetic flux induces an emf, ε = −ΔΦ/Δt (Faraday); Lenz's law fixes the direction, opposing the change. Motional emf is ε = Bℓv.
Traps
- Using degrees in sine terms for force on moving charges.
- Confusing series and parallel rules.
- Forgetting internal resistance when computing terminal voltage.
- Getting Lenz's law direction backwards.
- Treating potential as a vector.
Worked rule of thumb
For a circuit, first find the total equivalent resistance, then total current from the source, then work back to branch currents.