Consider three concentric metallic spheres A, B and C of radii a, b, c respectively where `a lt b lt c`, A and B are connected whereas C is grounded. The potential of the middle sphere B is raised to V then the charge on the sphere C is–

Options

A. `-4 pi epsilon_0 V (bc)/(c-b)`
B. `+4 pi epsilon_0 V (bc)/(c-b)`
C. `-4 pi epsilon_0 V (ac)/(c-a)`
D. Zero

Answer

A

Explanation

`V=(Kq)/b+(KQ)/(c)implies (K(q+Q))/c =0implies q+Q=0implies q=-Q`
`K/b(-Q)+(KQ)/c=VimpliesKQ(1/c-1/b)=V`
`implies Q = (bcV)/((b-c))4pi epsilon_0`
`=(-bcV)/((c-b))4piepsilon_0`