A charge q is placed at a distance of $\frac {a}{\sqrt {24}}$ above the centre of a horizontal, equilateral triangular surface of edge a. Find the flux of the electric field through the equilateral triangular surface.
Solution
Let us evaluate if we can have regular tetrahedron as the closed Gaussian surface.
The altitude of tetrahedron having side a is given by $H = a \sqrt {\frac {2}{3}}$
Distance of centroid from any face = $\frac {H}{4} = \frac {a}{\sqrt {24}}$
So, we can imagine a regular tetrahedron as the closed Gaussian surface with q placed at the centroid.
Total flux $= \frac {q}{\epsilon_0} = 4 \times $ flux though one surface
So, flux through one triangular surface $= \frac {q}{4\epsilon_0}$