Eight point charges of charge q each are placed on the eight corners of a cube of side a. A solid neutral metallic sphere of radius a/3 is placed with its center at the center of the cube. As a result, charges are induced on the sphere, which form certain patterns on its surface. What is the potential of the sphere?

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zero

$\frac{- 8}{\sqrt{3}} \frac{k q}{a}$

$\frac{16}{\sqrt{3}} \frac{k q}{a}$

$\frac{8}{\sqrt{3}} \frac{k q}{a}$

answer is B.

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Detailed Solution

Due to the induced charges of sphere, its potential will remain zero because net induced charge is zero. Potential of sphere will be due to only eight discrete charges. $V = 8 \frac{k q}{(\sqrt{3} a / 2)} = \frac{16 k q}{\sqrt{3} a}$

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