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Electric and Magnetic Fields

H3 Physics hub for electric and magnetic fields: conductors in electrostatics, Gauss’s law, Ampère’s law, electric dipoles, and magnetic dipoles.

  • GCE A-Level H3 Physics 2027
Learning goals
  • show an understanding that ideal conductors form an equipotential volume, and that the electric field within an ideal conductor is zero
  • show an understanding that electric charge accumulates on the surfaces of a conductor, and that the electric field at the surface of a conductor is normal to the surface
  • recall and apply Gauss’s law 6 for electric and magnetic fields (knowledge of the differential form of Gauss’s law is not required), and
  • recall and apply Ampère’s law 7 relating the line integral of the magnetic field (in a vacuum) around a closed loop with the electric current enclosed by the loop to solve problems involving symmetric field configurations (knowledge of the differential form of Ampère’s law is not required) [Note further that candidates are not required to know Maxwell’s generalisation of Ampère’s law including the term related to the rate of change of electric flux, nor the Biot-Savart law.]
  • solve problems involving symmetric charge distributions by relating the electric flux (in a vacuum) through a closed surface with the charge enclosed by that surface (ii) show an understanding that the magnetic flux through a closed surface is always zero, suggesting the non-existence of magnetic monopoles
  • define the magnitude of the electric dipole moment as the product of the charge and the separation
  • show an understanding of and use the torque on an electric dipole and the potential energy of an electric dipole to solve related problems
  • define the magnitude of the magnetic dipole moment for a current loop as the product of the current and the area of the loop
  • show an understanding of and use the torque on a magnetic dipole and the potential energy of a magnetic dipole to solve related problems

This topic recasts electric and magnetic field laws in integral form. The central skill is not integration alone: it is recognising symmetry, choosing a useful surface or loop, and stating why the field can be taken outside the integral.

Choose your route

Start with electric fields in conductors, then follow the ordered lessons on this hub. Each lesson adds a method needed by the next.

Start Here

You should already be comfortable with:

Who this hub is for

Use this hub if you are confident with H2 field ideas but need a reliable method for choosing Gaussian surfaces, Amperian loops, and dipole directions in H3 problems.

How this hub fits the broader H3 track

It is the first H3 electricity-and-magnetism topic. The five lessons build in order: electrostatic conductors establish boundary behaviour; Gauss’s and Ampère’s laws develop integral methods; electric dipoles then provide the model used to introduce magnetic dipoles.

Deep-dive lessons

  1. Electric Fields in Conductors — explain zero internal field, equipotential volume, surface charge, and the normal surface field.
  2. Gauss’s Law — relate closed-surface flux to enclosed charge and select surfaces using symmetry.
  3. Ampère’s Law — relate magnetic-field circulation to enclosed steady current in symmetric configurations.
  4. Electric Dipoles — use dipole moment, torque, and potential energy in a uniform electric field.
  5. Magnetic Dipoles — transfer the dipole model to a current loop and identify the analogy’s limit.
A useful decision rule

Ask what the source symmetry keeps unchanged. Use a closed surface for flux and enclosed charge, a closed path for circulation and enclosed current, and an energy model for dipole orientation or slow rotation.

Revision

Quick Reference
  • Gauss’s law (electric): ∮ E · dA = Q_encl/ε₀.
  • Gauss’s law (magnetic): ∮ B · dA = 0.
  • Ampère’s law (steady currents, vacuum): ∮ B · dl = μ₀ I_encl.
  • Electric dipole: p = qd, τ = p × E, U = -p · E.
  • Magnetic dipole: μ = NIA, τ = μ × B, U = -μ · B.
Problem Templates

Gauss’s law (fast field finding)

  1. Identify symmetry (spherical/cylindrical/planar).
  2. Choose a closed surface whose contributing regions have constant |E| and a known angle to dA.
  3. State which parts contribute, then evaluate ∮ E · dA.
  4. Set the result equal to Q_encl/ε₀ and solve for E.

Ampère’s law (fast B finding)

  1. Identify symmetry (e.g., long straight wire, solenoid).
  2. Choose an Amperian loop where |B| is constant on contributing segments.
  3. Evaluate ∮ B · dl and set it equal to μ₀ I_encl.
  4. Use the right-hand rule for direction.
Top Exam Traps
  1. Picking a Gaussian surface that does not match the symmetry (makes E vary and breaks the shortcut).
  2. Using total charge/current instead of the enclosed charge/current.
  3. Confusing the outward normal dA with the tangential path element dl.
  4. Assuming zero net flux or circulation means the field is zero at every point.
  5. Mixing up dipole-moment direction (from − to + for p) and torque direction.

Practice

Practice (Past-Year + Self-Check)
  • Do at least 2 Gauss-law problems and 2 Ampère-law problems where symmetry is the key.
  • For dipoles, sketch U(θ) = -pE cos θ and interpret stable versus unstable equilibrium.
H3 Paper Map (9814)

Continue learning

Next, study RLC Circuits, where capacitors and inductors turn electromagnetic energy storage into circuit dynamics.

Course and syllabus information
Course
GCE A-Level H3 Physics
Edition
GCE A-Level H3 Physics 2027