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CEGEP • Montreal

Electricity and Magnetism, 203-SN2-RE (formerly 203-NYB)

Electricity and Magnetism asks you to reason about fields, objects that no everyday experience makes intuitive. The course is 203-SN2-RE in the revised Science program (200.B1), formerly 203-NYB. Its detailed content varies from one CEGEP to another: some stop at RC circuits and Faraday's law, others keep electric flux (Gauss's law) and inductance. Every set on this page is on the syllabus of at least one CEGEP's version of the new course.

10 fully corrected exercise sets (137 exercises), 10 revision sheets, and 2 practice papers. Free, no account needed. The same course in French.

Measurement in the lab

  1. 1 Lab measurements, uncertainties and graphical analysis The experimental side of the electricity and magnetism course, in fifteen exercises built on the setups of the course. The basics: reading a digital multimeter and its datasheet, Ohm's law as a quotient, series and parallel, the extreme-values method on dissipated power, the differential method on the field of a solenoid. The problems: repeated voltage readings and the point where repeating stops helping, linearizing Ohm's law and the point that drops off when the resistor heats up, five statements to correct, emf and internal resistance by extreme lines, the time constant of an RC circuit by semi-logarithmic regression. The classics: random or systematic error and the loading effect of the voltmeter, colour code and tolerance, the Wheatstone bridge as a null method, the resistivity of a wire where the diameter counts twice, and the small difference of two voltages that costs a factor of four. Sheet

Electrostatics

  1. 2 Electric charge, field and potential Quantized charge compared with gravitation, the point where the field is zero, the scalar potential and its trap, the energy of a system of charges with equipotentials, an electron accelerated between two plates. Then an exam-level part: the net field by components, the ring and the rod where the sum becomes an integral, Gauss's law from the insulating sphere to the Faraday cage, the Millikan oil drop and the electron gun of a cathode-ray tube. A Part C adds three guided derivations: the field of a uniformly charged cylinder by Gauss's law, the potential difference of a point charge from the circulation of the field, and the potential of the cylinder, where infinity can no longer serve as the reference. Sheet
  2. 3 Gauss's law The flux through a cube, with the charge at the centre and then at the corner where the solid angle does all the work, the solid insulating sphere whose field grows with r before falling off as 1 over r squared, the coaxial cable and its shielding property, infinite planes taken one at a time and then in pairs, and a non-uniform charge density that rules out any memorized formula. Then an exam-level part: the off-centre cavity whose interior field is uniform, the factor of two that separates a charged sheet from a conductor, five statements to correct, Faraday's ice pail that measures a charge without touching it, and the atmospheric electric field that would drain the Earth in five minutes. Sheet
  3. 4 Electric potential and capacitors Potential that adds like a number and not like an arrow, with the point where V vanishes while the field does not, going from V to E by the gradient on a function of three variables, the potential of a ring and of a disk found by integration, the conductor in equilibrium with its cavity and its three regions, and two spheres joined by a wire that prove the point effect. Then an exam-level part: the parallel-plate, cylindrical and spherical capacitances derived, a network of four capacitors taken apart in both directions, five statements to correct, the energy stored in the field itself and the force between the plates, and a Van de Graaff generator taken all the way to the spark. Sheet

Direct-current circuits

  1. 5 Direct-current circuits Current and resistivity, the electron drift of 0.1 mm per second in a wire and the filament that burns out at switch-on, a series-parallel network with a power balance, emf and internal resistance, a two-loop circuit solved with Kirchhoff's laws with a negative current to interpret. Then an exam-level part: combinations of capacitors, a parallel-plate capacitor and its dielectric depending on whether the battery stays connected, the voltage divider and maximum power transfer, the ammeter, the voltmeter and the Wheatstone bridge, and the charging of the RC circuit. Sheet
  2. 6 RC circuits in direct current The RC circuit chapter as the revised Electricity and Magnetism course prescribes it, in fifteen exercises. The basics: charging a capacitor, the differential equation of the discharge, the time constant the capacitor sees when two resistors share the circuit, Kirchhoff's laws at the initial instant and in steady state, energy dissipated by Joule heating. The problems: a capacitance measured by the half-life and the voltmeter trap, the pacemaker, five statements to correct, the intermittent windshield wiper, the defibrillator. The classics: capacitors in series and in parallel, the debounce filter, the DRAM memory cell, a capacitor stopwatch, and how the energy is shared between two resistors. Sheet

Magnetism and induction

  1. 7 Magnetism and induction Magnetic force and the right-hand rule, circular motion with a period independent of speed, the velocity selector and the mass spectrometer that identifies carbon 12, the Laplace force and parallel wires, the torque on a loop with the motor and the galvanometer. Then an exam-level part: the Hall effect that reveals the sign of the carriers, the helical path of the polar auroras and the cyclotron up to its relativistic limit, the rod on rails, Faraday's coil, and the alternator with eddy currents. Sheet
  2. 8 Electromagnetic induction The flux calculated in three geometries, one of them by integration next to a wire, six Lenz's law situations to settle down to the sign, Faraday's law applied to a field that rises and then falls, with the emf vanishing exactly when the field is at its maximum, the rotating rod and the Faraday disk, and the mutual inductance of two coils with its coupling coefficient. Then an exam-level part: the induced electric field and the loop where the voltage depends on the path, the transformer and its reflected impedance, five statements to correct, the inductive sensor of an anti-lock braking system that goes blind at low speed, and the induction cooktop whose power grows as the square of the frequency. Sheet
  3. 9 Sources of the magnetic field The Biot-Savart law and the loop seen at angle alpha, the field at the centre of a coil and the hydrogen electron that creates 12.5 T, current arcs and the finite-length wire, Helmholtz coils and their nearly uniform field, the straight wire and the point of zero field. Then an exam-level part: the solenoid derived with a rectangular loop, the toroid and the current sheet, the coaxial cable region by region, the iron core with saturation and hysteresis, and the displacement current that closes Maxwell's four equations on the speed of light. Sheet

Transients, oscillations and AC circuits

  1. 10 RC, RL and RLC circuits Charging a capacitor with the differential equation and the half of the energy lost whatever the resistance, the 9 kW flash, the two capacitors that lose half their energy without losing a single charge, the RL circuit and the 600 V spark on opening, inductance calculated from geometry. Then an exam-level part: LC oscillations and the mass-spring analogy, RLC damping and critical resistance, sinusoidal steady state with reactances, impedance and phase shift, series resonance with voltage magnification and quality factor, and continuity at switching. Sheet

When the chapters are done

A full paper under exam conditions, on the whole course. Do it once every chapter is behind you: it measures what you can do on a question you have never seen.

Practice exam

Practice final exam: electricity and magnetism, extended course, 203-SN2-RE

A 3-hour final exam on the whole Electricity and Magnetism course, 12 exercises for 100 marks in four parts of 25, with a figure for nearly every question. Electrostatics: two charges, with the zero-field point set against the zero-potential point; a charged sphere handled with Gauss's law and the field curve; a charged ring whose field is proved maximal at a distance of the radius divided by root two. Circuits: a series-parallel network with a complete power balance, an unbalanced Wheatstone bridge solved with an equivalent source, a supply cable with line losses, minimum gauge and the effect of temperature. Magnetism: a proton accelerated and then bent, with a period independent of speed; a coil pulled out of the field and the energy balance behind Lenz's law; a toroid taken from Ampère's law to the magnetic energy recovered through the energy density. Regimes: an RL circuit and the continuity of the current, the sinusoidal regime with the impedance triangle, resonance and overvoltage, and five false claims to correct.

  • 12 questions
  • 100 points
  • 180 minutes
Sit the paper

Practice exam

Practice final exam: electricity and magnetism, 203-SN2-RE

A three-hour final exam, twelve exercises worth 100 marks, modelled on the revised Electricity and Magnetism syllabus: electrostatics by components, potential and energy, a deflected ink drop, a two-source network, a heating element, charging then discharging a capacitor, a current balance, a solenoid and a compass, a deflected electron beam, Faraday's law, a nonlinear field and checking a resistor in the lab. No Gauss's law or RL circuits, which some CEGEPs still teach: the dedicated series cover them.

  • 12 questions
  • 100 points
  • 180 minutes
Sit the paper

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