Potential at the centroid of an equilateral triangle of side ‘a’,

Question

Potential at the centroid of an equilateral triangle of side ‘a’, when equal charges each of magnitude ‘Q’ are placed at the vertices of the triangle is?

Options:

A . Zero

B . 14πϵ03Qa

C . 14πϵ03√3Qa

D . 14πϵ0Q√3a

Answer: Option C
:
C

V^{1} = V_{1} + V_{2} + V_{3}; V_{1} = V_{2} = V_{3}

= 3 V_{1}

= 3 \frac{1}{4 π ϵ_{0}} \frac{Q}{\frac{a}{\sqrt{3}}}

= \frac{1}{4 π ϵ_{0}} \frac{3 \sqrt{3 Q}}{a}

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