Question

Two concentric hollow conducting spheres of radius r and R are shown. The charge on outer shell is Q. What charge should be given to inner sphere so that potential at any point P outside the outer sphere is zero?
a) -Qr/R
b) -QR/r
c) -Q
d) -2QR/r​

Answer 1

i think the answer is -Q as the sum of potential must be zero outside the outer sphere.

Answer 2

Answer:

The charge on inner sphere should be  -Q.

(c) is correct.

Explanation:

Given that,

Two concentric hollow conducting spheres of radius r and R. The charge on outer shell is Q.

Let the charge on inner sphere is q.

The potential on outer surface for outside point

$R>r$

$V= \dfrac{Q}{4\pi\epsilon_{0}R}+\dfrac{q}{4\pi\epsilon_{0}R}$

The potential at any point P outside the outer sphere is zero.

$0=\dfrac{Q}{4\pi\epsilon_{0}R}+\dfrac{q}{4\pi\epsilon_{0}R}$

$\dfrac{-Q}{4\pi\epsilon_{0}R}=\dfrac{q}{4\pi\epsilon_{0}R}$

$q = -Q$

Hence, The charge on inner sphere should be  -Q.