Question

Two concentric conducting spheres are of radii $r_1$ and $r_2$. The outer sphere is given a charge $q$. The charge $q^{\prime }$ on the inner sphere will be (inner sphere is grounded) :-

• A. $q$
• B. $-q$
• C. $-q\frac{r_1}{r_2}$
• D. Zero

Answer 1

The correct option is C $-q\frac{r_1}{r_2}$


Due to earthing, potential of inner sphere in zero
$V=0$
$\frac{Kq}{r_2}+\frac{K{q}^{\prime }}{r_1}=0\Rightarrow q^{\prime }=-\frac{q{r}_1}{r_2}$