Question

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 $\frac{a}{3}$ is placed with its centre at the centre of the cube. As a result, charges are induced on the sphere, which form a certain pattern on its surface. The electric potential of the sphere is

• A. $\frac{-12}{-\sqrt{3}} \frac{ Kq }{a}$
• B. $\frac{18}{\sqrt{4}} \frac{ Kq }{ a }$
• C. $-\frac{8}{\sqrt{2}} \frac{ Kq }{ a }$
• D. $\frac{16}{\sqrt{3}} \frac{ Kq }{ a }$

Answer 1

Answer: (D)

Net induced charge on sphere is zero so its potential at its own centre will be zero.
$V_0$ = potential due to charges placed at eight corners
$V _{0}=\frac{8 Kq }{(\sqrt{3} / 2) a } \Rightarrow V _{0}=\frac{16 Kq }{\sqrt{3} a }$