Question

Two metallic spheres of radii $2cm$ and $6cm$ are given charges $3\times {10}^{-2}C$ and $7\times {10}^{-2}C$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

• A. $7.5\times {10}^{-2}C$
• B. $4\times {10}^{-2}C$
• C. $3.5\times {10}^{-2}C$
• D. $2\times {10}^{-2}C$

Answer 1

The correct option is A $7.5\times {10}^{-2}C$

After connection voltage will be same on both spheres

$V_1^1=\frac{k{q}_1^1}{r_1}=V_2^1=\frac{k{q}_2^1}{r}$

$q_1^1=\frac{q_2^1}{3}$

Let $q_1,q_2$ be the previous charge

$q_1+q_2=q_1^1+q_2^1$

$q_2^1=\frac{3}{4}(q_1+q_2)$

$q_2^1=7.5\times {10}^{-2}C$