Physics / advanced
Electrostatic structure and boundary methods
Solve electrostatic problems through uniqueness, Green functions, multipoles, and material interfaces rather than relying only on symmetric examples.
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Module 01 advanced
Electrostatic structure and boundary methods
Solve electrostatic problems through uniqueness, Green functions, multipoles, and material interfaces rather than relying only on symmetric examples.
- 01
Poisson’s equation and the promise of uniqueness
Use an energy identity to decide what an electrostatic solution must satisfy.
27 min - 02
Choose electrostatic boundary data consistently
Distinguish prescribed potential, normal derivative, and total conductor charge.
27 min - 03
Image charges replace a boundary, not the conductor
Use uniqueness to validate images and distinguish force from assembly energy.
27 min - 04
Resolve boundary structure into harmonic modes
Derive spatial decay of boundary patterns in a grounded strip.
27 min - 05
Build a Green function with a declared convention
Track normalization, boundary terms, and the Neumann zero mode.
27 min - 06
State the convention before computing a multipole
Connect normalized angular coefficients with physical charge moments and radial decay.
27 min - 07
Make capacitance a matrix with a reference
Connect reciprocity, grounding, floating conductors, and positive field energy.
27 min - 08
Match the right field components at a dielectric interface
Use displacement for free charge and electric field for total charge.
27 min - 09
Let shape determine the depolarizing field
Connect bound surface charge with internal fields and dielectric self-consistency.
27 min - 10
Differentiate the energy for the imposed electrical constraint
Track source work to reconcile fixed-charge and fixed-voltage forces.
27 min