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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

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Flux Through Triangular Surface

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 $= \frac {q}{4\epsilon_0}$