Preparation for the International Physics Olympiad (IPhO): Electromagnetism

The IPhO syllabus includes:

2.3 Electromagnetic fields
  • 2.3.1 Basic concepts: Concepts of charge and current; charge conservation and Kirchhoff's current law. Coulomb force; electrostatic field as a potential field; Kirchhoff's voltage law. Mag­netic B-field; Lorentz force; Ampere's force; Biot-Savart law and B-field on the axis of a circular current loop and for simple symmetric systems like straight wire, circular loop and long solenoid.
  • 2.3.2 Integral forms of Maxwell's equations: Gauss' law (for E- and B-fields); Ampere's law; Faraday's law; using these laws for the calculation of fields when the integrand is almost piecewise constant. Boundary conditions for the electric field (or electrostatic potential) at the surface of conductors and at infinity; concept of grounded conductors. Superposition principle for elec­tric and magnetic fields; uniqueness of solution to well- posed problems; method of image charges.
  • 2.3.3 Interaction of matter with electric and magnetic fields; Resistivity and conductivity; differential form of Ohm's law. Dielectric and magnetic permeability; relative per­mittivity and permeability of electric and magnetic ma­terials; energy density of electric and magnetic fields; fer­romagnetic materials; hysteresis and dissipation; eddy currents; Lenz's law. Charges in magnetic field: helicoidal motion, cyclotron frequency, drift in crossed E- and B-fields. Energy of a magnetic dipole in a magnetic field; dipole moment of a current loop.
  • 2.3.4 Circuits: Linear resistors and Ohm's law; Joule's law; work done by an electromotive force; ideal and non-ideal batter­ies, constant current sources, ammeters, voltmeters and ohmmeters. Nonlinear elements of given V-I charac­teristic. Capacitors and capacitance (also for a single electrode with respect to infinity); self-induction and in­ductance; energy of capacitors and inductors; mutual in­ductance; time constants for RL and RC circuits. AC circuits: complex amplitude; impedance of resistors, in­ductors, capacitors, and combination circuits; phasor di­agrams; current and voltage resonance; active power.
Members of the Spanish National Team can download the course notes here:
Some cognitive conflicts involving Electromagnetism:
It is also useful to follow the IPhO's Study Guide by Jaan Kalda
Here you can find the solutions to some of the problems:

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