D. J. Griffiths, Introduction to Electrodynamics, 4th ed., Ch. 7 (Electrodynamics).
Faraday induction, motional emf, induced electric fields, displacement current, Maxwell equations and conservation.
EM-03
Course overview
Maxwell equations, continuity & electromagnetic energy
Extend the static E and B models to induction, displacement current, complete Maxwell equations, charge conservation and the Poynting energy balance. Every derivation distinguishes a fixed contour from a moving conductor, prescribed from induced fields, and instantaneous from quasistatic approximations.
5/5available
Prerequisites
- EM-01: electric field and potential
- EM-02: magnetic fields and inductance
- Circulation, flux, surface integrals and cross products
Course outcomes
- Calculate time-varying-flux and moving-conductor emf.
- Derive Ampère–Maxwell and charge continuity.
- Organize Maxwell's equations and their validity ranges.
- Derive Poynting's theorem and electromagnetic power balances.
Syllabus
Maxwell equations, continuity & electromagnetic energy
Extend the static E and B models to induction, displacement current, complete Maxwell equations, charge conservation and the Poynting energy balance. Every derivation distinguishes a fixed contour from a moving conductor, prescribed from induced fields, and instantaneous from quasistatic approximations.
- 01→
Faraday induction
Separate transformer emf from motional emf with an explicit oriented-loop convention: derive ∮E·dl=−dΦB/dt for a fixed contour, apply Lenz's law as a consequence of the signed flux rule, calculate induced azimuthal E for a changing axial B, derive the moving-rod emf from qv×B, reconcile both mechanisms via a moving-loop flux rule and account for mechanical versus Joule power.
250–310 min · Intermediate → advanced · available - 02→
Displacement current
Derive the Ampère–Maxwell correction from continuity and Gauss's law, resolve the two-spanning-surfaces charging-capacitor problem, compute the changing-flux contribution across complete and partial plate areas, separate displacement current from charge transport, and extend from vacuum E/B to free current, D and H in matter without confusing polarization and conduction.
230–290 min · Intermediate → advanced · available - 03→
Maxwell equations
Assemble all four vacuum Maxwell equations in local and fixed-surface integral form, keeping enclosed charge and signed current distinct; derive source-free wave equations and transverse plane-wave constraints, show the finite vacuum wave speed and correctly orient E, B and propagation. State boundary, material and quasistatic limits before applying simplified field laws.
270–330 min · Intermediate → advanced · available - 04→
Charge continuity
Derive the integral and differential charge-conservation laws for fixed and moving control volumes, including normal-current signs, surface charge accumulation and sheet currents at interfaces. Relate continuity to Ampère–Maxwell and demonstrate terminal charge balances for a capacitor and a confined two-dimensional conductor without double-counting displacement and transport.
250–320 min · Intermediate → advanced · available - 05→
Poynting theorem & electromagnetic energy
Derive the local and fixed-volume Poynting energy balance from Maxwell's curl equations, distinguishing field storage, outward electromagnetic flux and work on material charges. Compute energy transport in vacuum plane waves and energy delivery to a charging capacitor, then identify the limitations of naive stored-energy formulas in lossy, nonlinear and dispersive matter.
270–330 min · Intermediate → advanced · available
Reference backbone
References
Textbook electrodynamics and SI conventions for induced fields and power balances.
E. M. Purcell & D. J. Morin, Electricity and Magnetism, 3rd ed., chapters on induction.
Induction experiments, flux orientation, current direction and moving conductors.
J. D. Jackson, Classical Electrodynamics, 3rd ed., Chs. 5–6.
Magnetic fields, electromagnetic induction and continuum electromagnetic energy.
BIPM, The International System of Units (SI), 9th ed.
Units of electric field, magnetic flux (weber), electromotive force and electromagnetic power.