Electric fields due to different kinds of plates

We have a triangular uniformly charged plate of charge density \(\sigma\).

We take a point just above a vertex of the triangular plate at a distance \(d\) perpendicular to the plane of the triangle. Let the vertical component of electric field at that point be \(E(d)\) in \(V/m\)

Find \( \displaystyle \lim_{d \rightarrow 0}{E(d)} \)

Details and Assumptions:

1) \( \sigma = 10^{-9} C , {\epsilon}_{0}=8.85 \times {10}^{-12} \text{ SI units} \)

2) The triangle is equilateral. By vertical component of electric field I mean electric field perpendicular to the plane of charge.

3) The plate is non conducting.

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