Question

Two metallic spheres of radii $2\text{cm}$ and $14\text{cm}$ are connected by a conducting wire. If the sum of charges on both the spheres is $8\text{C}$, then the charge on the smaller sphere is :

• A. $4\text{C}$
• B. $3\text{C}$
• C. $2\text{C}$
• D. $1\text{C}$

Answer 1

The correct option is D $1\text{C}$

Let the charge on the bigger and smaller sphere be $Q_1$ and $Q_2$ respectively.

According to the question :
$Q_1+Q_2=8\text{C}$ ------$\left(1\right)$

Since, the spheres are connected by a conducting wire, there electric potential will be same.
i.e. $V_1=V_2$

$\Rightarrow \frac{k{Q}_1}{R_1}=\frac{k{Q}_2}{R_2}$

From the data given the question :
$\frac{Q_1}{14}=\frac{Q_2}{2}$

Or, $Q_1=7Q_2$

Putting in $\left(1\right)$ :
$7Q_2+Q_2=8$

Or, $Q_2=1\text{C}$