= Fringing field of a capacitor
= Capacitor fringing field
{synonym}
The <fringing field of a capacitor> is the nonuniform <electric field> near the edges of its <electrical conductors>, extending outside the gap. For a <parallel-plate capacitor>, neglecting it is useful when the gap is much smaller than both plate widths; the approximation $C\simeq\epsilon A/d$ is less reliable when these lengths become comparable.
Finite plates break the translational <symmetry> of the infinite-plate model. Each <conductor in electrostatic equilibrium> is an <equipotential>, so the <electric field> must meet a smooth conducting surface normally. Near an edge, the <equipotentials> curve into the surrounding space and the <electric field> changes both direction and magnitude. The <surface charge density> adjusts to enforce the conducting <boundary conditions>; it is not uniform all the way to a sharp edge. The <electrostatic boundary conditions at a conductor> explain why zero <electric field> inside the metal does not imply zero <electric field> just outside it.
The practical issue is where the nearly uniform region ends. A probe near the centre can support $E\simeq V/d$ while a probe close to an edge detects a lateral component and a different magnitude. A total <capacitance> reading also includes <electric flux> outside the simple footprint. The <fringing field of a capacitor> can therefore matter in <permittivity> measurements even when a central <electric field> measurement looks nearly ideal. Keysight's three-<electrode> fixture diverts the fringe contribution away from the measured response.<Materials Measurement: Dielectric Materials>[Solution: fringe capacitance and the three-electrode 16451B fixture]{ref}
\Image[/capacitor-fringing-field-and-guard-electrode.png]
{title=Finite-plate <electric field> and a separate <guard electrode of a capacitor>}
{description=Left: original <bounded two-dimensional capacitor field model> with $d/W=0.25$, showing computed <equipotentials> and <electric field> direction. The visible window is a crop of the stated bounded domain. Right: a conceptual cross-section through a surrounding guard ring, with an insulated central sensing <electrode>; the arrows are schematic, not a computed guarded solution. Neither panel is measured data.}
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