= Solution
Strong <homeotropic anchoring> requires radial orientation just outside a sphere, while the remote director is uniform. A plausible \b[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.<Director field configurations around a spherical particle in a nematic liquid crystal by Holger Stark>[1999, configuration comparison and dependence on particle/surface parameters]{ref}
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