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First-year university electromagnetism

Study first-year university electromagnetism through charge, fields, potential, circuits and magnetic forces, with optional induction and A.C. lessons.

  • University Physics Year 1
  • 57 lessons
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Before you begin

UY1 electromagnetism trains method selection: when to use field symmetry, when to switch to potential-energy arguments and when circuit approximations are valid. Explain your assumptions before you calculate.

Be comfortable with: A-Level electric fields and current electricity, and the integrals in mathematics for undergraduate physics.

Learning goals
  • Analyse capacitance, resistance, energy transfer, and transient circuit behaviour.
  • Construct electric-field and potential models for discrete and continuous charge distributions.
  • Analyse magnetic forces, induction, inductance, and alternating-current systems with consistent signs.

Lessons

Work through them in order.

  1. Capacitors and capacitanceDefine capacitance and derive the parallel-plate formula from its geometry.
  2. Capacitors in series and parallelDerive the equivalent capacitance of series and parallel combinations from charge and voltage.
  3. Energy stored in capacitorsDerive the energy a capacitor stores and the energy density of an electric field.
  4. Electric field linesDraw and read electric field lines as a map of field direction and strength.
  5. Electric field of a point chargeDerive the field of a point charge from Coulomb's law and add fields as vectors.
  6. Electric potentialDefine electric potential and potential difference and compute them for point-charge systems.
  7. Electric potential energyRelate electric work to potential energy in uniform fields and point-charge systems.
  8. Equipotential surfacesExplain why equipotential surfaces are perpendicular to the field and why a conductor's surface is one.
  9. Potential gradientFind the electric field from the potential gradient, including its components.
  10. Gauss’s law: flux and closed surfacesDefine electric flux and state Gauss's law for a closed surface.
  11. Gauss’s law for conductorsUse Gauss's law to show that charge sits on a conductor's surface and the field there is normal.
  12. Interpreting enclosed charge in Gauss’s lawApply Gauss's law to negative, zero and multiple enclosed charges.
  13. Gauss’s law for common charge distributionsUse Gauss's law to find the fields of an infinite line, an infinite sheet and parallel plates.
  14. Resistance and resistivityDistinguish resistance from resistivity, derive R = ρ L/A and account for temperature.
  15. Resistance of a cylindrical resistorApply R = ρ L/A to cylindrical conductors and scale resistance with radius.
  16. RC circuitsDerive the charging and discharging equations of an RC circuit and interpret its time constant.
  17. RL circuitsDerive current growth and decay in an RL circuit and use its time constant.Supporting
  18. Electric charge and Coulomb’s lawApply Coulomb's law in vector form and superpose forces from several charges.
  19. Solving Coulomb’s law problemsFollow a step-by-step method for Coulomb-force problems, including vector addition and checks.Supporting
  20. From Coulomb’s law to Gauss’s lawDerive Gauss's law for a point charge from Coulomb's inverse-square field.
  21. Electric dipolesDefine dipole moment and derive the torque and potential energy of a dipole in a uniform field.
  22. Electric field of a dipoleDerive the field of a dipole on its axis and bisector, exactly and far away.
  23. Electric field of a line of chargeIntegrate to find the field of a finite line of charge, using symmetry to cancel components.
  24. Electric field of a ring of chargeIntegrate to find the on-axis field of a charged ring and check its limits.
  25. Electric field of two oppositely charged infinite sheetsSuperpose sheet fields to find the field between and outside two oppositely charged sheets.
  26. Electric field of a uniformly charged diskSum ring contributions to find the on-axis field of a charged disk, with sheet and point limits.
  27. Field and potential of a charged conducting sphereFind the field and potential inside and outside a charged conducting sphere.
  28. Electric field of a uniformly charged sphereUse Gauss's law to find the field inside and outside a uniformly charged insulating sphere.
  29. Potential energy of several point chargesCompute the potential energy of a multi-charge system by summing over pairs.
  30. Electric potential of a ring of chargeDerive the on-axis potential of a charged ring and check it against the field.
  31. Electric potential of a line of chargeDerive the potential of a finite line of charge and differentiate it to find the field.
  32. Electric potential of an infinite line chargeExpress the potential of an infinite line charge from a reference radius and recover its field.
  33. Capacitance of a spherical capacitorDerive the capacitance of concentric spherical conductors and interpret its limits.
  34. Capacitance of a cylindrical capacitorDerive the capacitance per unit length of a coaxial cylindrical capacitor with Gauss's law.
  35. Dielectrics in capacitorsExplain how a dielectric changes capacitance, field, voltage and stored energy, with and without a battery.
  36. Energy stored in a spherical capacitorFind the energy of a spherical capacitor from its capacitance and by integrating field energy density.
  37. Sharing charge and energy between capacitorsSolve charge-sharing problems with charge conservation and account for the energy lost.
  38. Current, drift velocity and current densityRelate current, drift velocity and current density with consistent carrier signs.
  39. E.m.f. and power in circuitsModel a real source by its e.m.f. and internal resistance, and find terminal voltage and power.
  40. Charged-particle motion in magnetic fieldsUse the magnetic Lorentz force to predict straight, circular and helical particle paths.
  41. The Hall effectDerive the Hall voltage and use it to find the sign and density of charge carriers.
  42. Magnetic force on a current-carrying wireCompute the magnetic force on straight wires and current elements in vector form.
  43. Force and torque on a current loopShow that a uniform field exerts no net force but a torque τ = μ × B on a current loop.
  44. Magnetic field of a current elementApply the Biot–Savart law to find the magnetic field of a current element.
  45. Magnetic field of a straight current-carrying wireFind the magnetic field around a long straight wire and its direction.
  46. Magnetic field of a circular current loopFind the magnetic field at the centre and on the axis of a circular current loop.
  47. Magnetic field of a moving chargeCalculate the magnetic field of a moving point charge using the cross product.
  48. Magnetic forces between parallel conductorsDerive the force per unit length between parallel currents and predict attraction or repulsion.
  49. Magnetic force on a curved conductorFind the net magnetic force on a wire with straight and curved sections in a uniform field.
  50. Magnetic field lines and magnetic fluxCalculate magnetic flux through a surface and apply Gauss's law for magnetism.
  51. Magnetic energy in an inductorDerive the energy stored in an inductor and the energy density of a magnetic field.
  52. Electromagnetic induction experimentsUse coil-and-magnet experiments to show that induction needs a changing magnetic flux.
  53. Phasors and alternating currentsRepresent A.C. signals as phasors, combine them and compute r.m.s. values.
  54. Resistors, inductors and capacitors in A.C. circuitsCompare resistors, inductors and capacitors in A.C. circuits by phase, reactance and average power.
  55. Electromagnetic spectrum and sinusoidal plane wavesPlace radiation on the electromagnetic spectrum and describe a sinusoidal plane wave's fields.
  56. Energy and momentum in electromagnetic wavesCalculate energy density, the Poynting vector, intensity and radiation pressure of an electromagnetic wave.
  57. Understanding electric fields through test chargesBuild the idea of an electric field from the force on a test charge and superpose fields.

Practise and check

Recommended nextElectromagnetism topic check

Topic reference

Induction, inductance and A.C. circuits

These pages continue the module into Ampère’s law, induction and A.C. circuits.