D. J. Griffiths, Introduction to Electrodynamics, 4th ed., Ch. 5 (Magnetostatics).
Magnetic force on charges and current elements, current-density definitions, and magnetic-field geometry; later chapters cover Biot–Savart and Ampère.
EM-02
Course overview
Magnetic field & magnetostatics
Magnetic force first fixes what a magnetic field does; stationary currents then supply source laws for calculating that field. We progress from moving charges through Biot–Savart and Ampère to vector potential, inductance and magnetic energy, without confusing steady-source assumptions with arbitrary time dependence.
5/5available
Prerequisites
- EM-01: electric field and potential
- Vector cross product and Newtonian motion
- Vector calculus basics and SI units
Course outcomes
- Calculate force on moving charges and current elements.
- Compute B via Biot–Savart and Ampère with justified symmetry.
- Introduce vector potential without confusing gauge and field.
- Derive inductance and magnetic-energy balances.
Syllabus
Magnetic field & magnetostatics
Magnetic force first fixes what a magnetic field does; stationary currents then supply source laws for calculating that field. We progress from moving charges through Biot–Savart and Ampère to vector potential, inductance and magnetic energy, without confusing steady-source assumptions with arbitrary time dependence.
- 01→
Lorentz force
Define the operational electric and magnetic force on a moving point charge, derive the cross-product geometry, prove that a static magnetic field does no mechanical work, solve constant-B circular/helical motion and carry the result to the force on a current element. Distinguish a force law for given fields from source laws for computing those fields.
220–280 min · Intermediate → advanced · available - 02→
Biot–Savart law
Compute magnetostatic B from a prescribed steady current: derive and interpret the filament and current-density integrals, identify source/observation coordinates and right-hand orientation, and integrate the finite and infinite straight wire and the on-axis circular loop. Distinguish the source law from the Lorentz force, specify steady divergence-free currents and the thin-filament idealization, and check signs, dimensions, limits and singular endpoints.
250–310 min · Intermediate → advanced · available - 03→
Ampère's law
From the magnetostatic curl equation to the integral circulation law, distinguish current enclosed from the local field on a chosen loop. Derive straight-wire, uniformly filled cylindrical conductor and ideal infinite current-sheet fields using actual symmetries; demonstrate why zero circulation or zero enclosed current is not a local zero-field criterion; identify the time-varying displacement-current correction.
240–300 min · Intermediate → advanced · available - 04→
Magnetic vector potential
Construct B as the curl of a vector potential and distinguish gauge freedom from physical magnetic flux. Under a declared stationary localized-current/Coulomb-gauge model, derive the vector Poisson equation and its Green-kernel solution, recover Biot–Savart by taking a curl, compare symmetric and Landau gauges for uniform B, and explain why infinite-wire potentials require a finite reference radius.
250–310 min · Advanced · available - 05→
Inductance and magnetic energy
Define oriented magnetic flux linkage and self/mutual inductance; derive reversible U=∫I dλ and ½LI² for fixed linear geometry, compute an ideal long-solenoid inductance and field-energy cross-check, obtain a rectangular-cross-section toroid's logarithmic result, and distinguish reciprocity, passivity, loss, nonlinear magnetic media and dispersion.
270–330 min · Advanced · available
Reference backbone
References
Core field texts are combined with SI units and explicit nonrelativistic limits.
E. M. Purcell & D. J. Morin, Electricity and Magnetism, 3rd ed., chapters on magnetic fields and forces.
Operational force laws, vector cross products and relative-motion context.
J. D. Jackson, Classical Electrodynamics, 3rd ed., Ch. 5.
Classical magnetostatic source laws, field derivations and the limits of static approximations.
BIPM, The International System of Units (SI), 9th ed.
SI definitions and consistent use of the tesla, newton, ampere, coulomb and volt.