Question

Three identical metallic uncharged spheres $A, B$, and $C$, each of radius $a$, are kept at the corners of an equilateral triangle of side $d(d>>a)$ as shown in figure. The fourth sphere (of radius $a$ ), which has a charge $q$, touches $A$ and is then removed to a position far away. $B$ is earthed and then the earth connection is removed. $C$ is then earthed. The charge on $C$ is

• A. $\frac{q a}{2 d}\left(\frac{2 d-a}{2 d}\right)$
• B. $\frac{q a}{2 d}\left(\frac{2 d-a}{d}\right)$
• C. $-\frac{q a}{2 d}\left(\frac{d-a}{d}\right)$
• D. $\frac{2 q a}{d}\left(\frac{d-a}{2 d}\right)$

Answer 1

Answer: (C)

$\frac{k q_{1}}{a}+\frac{k q}{2 d}=0$ or $q_{1}=\frac{-q a}{2 d}$
$\frac{k q_{2}}{a}+\frac{k q}{2 d}+\frac{k q_{1}}{d}=0$
or $q_{2}=\frac{-q a}{2 d}\left(\frac{d-a}{d}\right)$