Physics / advanced
Magnetic fields, circuits, and induction
Connect magnetic sources, vector potentials, induction, and magnetic materials while keeping local fields and circuit approximations distinct.
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Module 01 advanced
Magnetic fields, circuits, and induction
Connect magnetic sources, vector potentials, induction, and magnetic materials while keeping local fields and circuit approximations distinct.
- 01
Biot–Savart fields and current geometry
Build magnetic fields from complete steady-current geometries and identify the limits of an instantaneous source integral.
28 min - 02
Magnetic dipole fields and torque
Separate the distant dipole field, the singular ideal point source, and the torque of a small moment in an external field.
29 min - 03
Vector potential and gauge choice
Construct different potentials for the same magnetic field and preserve measurable quantities under a consistent gauge transformation.
29 min - 04
Magnetic boundary conditions and surface currents
Derive magnetic jumps with an explicit interface normal and distinguish free surface current from magnetization current.
30 min - 05
Inductance matrices and magnetic energy
Track winding orientations, signed mutual coupling, reciprocity, and the positivity constraints imposed by magnetic energy.
31 min - 06
Motional emf and moving circuits
Combine Lorentz force with the total flux derivative for a moving contour and reconcile mechanical work with electrical heating.
31 min - 07
Faraday induction and flux linkage
Relate circulating electric fields to changing flux and distinguish single-turn flux, winding linkage, and a lumped circuit response.
30 min - 08
Eddy currents and magnetic diffusion
Derive field diffusion in an Ohmic conductor, identify its assumptions, and connect spatial scale to decay time and skin depth.
32 min - 09
Magnetization and bound-current description
Convert a prescribed magnetization into equivalent currents and keep internal H, applied H, and physical B distinct.
31 min - 10
Hysteresis and magnetic work cycles
Interpret a material's magnetic history and compute cycle work from a B–H loop with the correct density units and sign convention.
32 min