Question

Two isolated spherical conductors have radii $5\text{cm}$ and $10\text{cm}$ respectively. They have charges of $12\mu \text{C}$ and $-3\mu \text{C}$. Find the charge on bigger sphere after they are connected by a conducting wire.

• A. $6\mu \text{C}$
• B. $3\mu \text{C}$
• C. $9\mu \text{C}$
• D. $4\mu \text{C}$

Answer 1

The correct option is A $6\mu \text{C}$

Total charge on the system $Q=Q_1+Q_2=12-3=9\mu C$

When charges are connected by conducting wire, charge redistribution happens until spheres are equipotential.

$\frac{k{Q}_1^{\prime }}{r_1}=\frac{k{Q}_2^{\prime }}{r_2}$

From conservation of charge $Q_1^{\prime }+Q_2^{\prime }=9\mu C$

So, charge on bigger sphere is,

$Q_1^{\prime }=\frac{r_1}{r_1+r_2}\times Q=\frac{10}{10+5}\times 9=6\mu \text{C}$