Three short electric dipoles, each of dipole moment P, are placed at the vertices of an equilateral triangle of side length L. Each dipole has its dipole moment oriented parallel to the opposite side of the triangle as shown in the figure. Find the electric field (E) and potential (V) at the centroid of the triangle

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E = 0

$V = \frac{6 k P}{L^{2}}$

$E = \frac{6 \sqrt{3} k P}{L^{3}}$

V = 0

answer is B, C.

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Detailed Solution

$\begin{array}{l} Centroid lies in equilateral position of dipole where V = 0 \\ \Rightarrow E = (1 + 2 \cos 60^{\circ}) \frac{k p}{{(\frac{\sqrt{3}}{2} L \frac{2}{3})}^{3}} \\ \Rightarrow E = \frac{6 \sqrt{3} k p}{L^{3}} \end{array}$

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