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 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

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 (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) (-12/-√3) ( Kq /a) (B) (18/√4) ( Kq / a ) (C) -(8/√2) ( Kq / a ) (D) (16/√3) ( Kq / a )

Tardigrade Admin · Accepted Answer

Net induced charge on sphere is zero so its potential at its own centre will be zero. V0 = potential due to charges placed at eight corners V 0=(8 Kq /(√3 / 2) a ) ⇒ V 0=(16 Kq /√3 a )

$\frac{- 12}{- 3} \frac{K q}{a}$

$\frac{18}{4} \frac{K q}{a}$

$- \frac{8}{2} \frac{K q}{a}$

$\frac{16}{3} \frac{K q}{a}$

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
$V_{0} = \frac{8 K q}{( 3 /2 ) a} \Rightarrow V_{0} = \frac{16 K q}{3 a}$

−3​−12​aKq​

4​18​aKq​

−2​8​aKq​

3​16​aKq​

Net induced charge on sphere is zero so its potential at its own centre will be zero. V0​ = potential due to charges placed at eight corners V0​=(3​/2)a8Kq​⇒V0​=3​a16Kq​

$\frac{- 12}{- 3} \frac{K q}{a}$

$\frac{18}{4} \frac{K q}{a}$

$- \frac{8}{2} \frac{K q}{a}$

$\frac{16}{3} \frac{K q}{a}$

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
$V_{0} = \frac{8 K q}{( 3 /2 ) a} \Rightarrow V_{0} = \frac{16 K q}{3 a}$