Edge Effect of Rectangular Parallel Plate Capacitor Calculator
This CalcTown calculator calculates the edge effect of a rectangular parallel plate capacitor.
The goal of this problem is to explore, in a crude sense, the correction to the capacitance C of a parallel plate
capacitor due to edge effects.
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L = length of the rectangular parallel plates
w = width of the rectangular parallel plates
d = dielectric thickness
Δt = increase in effective length and width due to edge effect
εr = relative permittivity
Edge Effect in a Capacitor
If d << √A, then on the length scale of d, near the edge of the capacitor, the capacitor looks like parallel semi-infinite plates separated by a distance d. Let us suppose that the upper plate is held at potential ϕ0/2, and is located at a distance y = d/2 above the x-axis; the lower plate is held at potential −ϕ0/2 and is located at y = −d/2. Suppose that δ0 is the change in capacitance per unit length associated with such a scenario.
We can approximateC/ε = A/d + Lδ
where, L is the perimeter of the capacitor plate.
To compute the edge effects, we use conformal mapping. Consider the transformation,z=dw/ϕ0 + de2Πw/ϕ0/2Π
Here z represents the spatial coordinate, and w the complex electric potential.
Thus we can write δ = 1/2Π * log(√A/d) + δ0
is an unknown constant (independent of d or A).