Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 2 / Section B / 22 / iii / c

Strong homeotropic anchoring requires radial orientation just outside a sphere, while the remote director is uniform. A plausible dipolar texture contains a compensating hyperbolic hedgehog defect on one side. The particle's radial boundary has charge $+1$ under a consistent convention, balanced by an exterior point defect of charge $-1$ so the far field is uniform. The original cross-section depicts this configuration.

An alternative has an equatorial Saturn-ring defect. Its local disclination winding is half-integer; that local winding is not itself the net three-dimensional compensating charge. Particle size, elastic constants, confinement and anchoring strength select between configurations. The elastic theory explicitly compares dipolar, Saturn-ring and surface-ring states.^[ref]