Question

Two isolated conducting spheres $S_1$ and $S_2$ of radius $\left(\frac{2}{3}\right)R$ and $\left(\frac{1}{3}\right)R$ have $12\mu C$ and $-3\mu C$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on $S_1$ and $S_2$ are respectively.

• A. $6\mu Cand3\mu C$
• B. $4.5\mu Conboth$
• C. $+4.5\mu Cand-4.5\mu C$
• D. $3\mu Cand6\mu C$

Answer 1

The correct option is D

$3\mu Cand6\mu C$

Given data:

The radius of spheres, $S_1=\frac{2}{3}R$

The radius of spheres, $S_2=\frac{1}{3}R$

Spheres charges of ${Q^{\text{'}}}_1=12\mu C$

Spheres charges of ${Q_2}^{\text{'}}=-3\mu C$

Calculation:

Formula used:

$Q_1+\hspace{0.17em}{Q}_2=Q{\text{'}}_1+\hspace{0.17em}Q{\text{'}}_2$

$=12\mu C-3\mu C$

$=9\mu C$

$\Rightarrow V_1=V_2$ (where V₁ and V₂ are velocities and K is constant)

$\Rightarrow \frac{KQ{\text{'}}_1}{{\displaystyle \frac{2R}{3}}}=\frac{KQ{\text{'}}_2}{{\displaystyle \frac{R}{3}}}$

Now,

$Q{\text{'}}_1=2Q{\text{'}}_2$

$\Rightarrow 2Q{\text{'}}_2+\hspace{0.17em}Q{\text{'}}_2=9\mu C$

$\Rightarrow Q{\text{'}}_2=3\mu C$

$Q{\text{'}}_1=6\mu C$

A long time after this is done the charges on $S_1$ and $S_2$ are respectively $Q{\text{'}}_1=6\mu C$ and $Q{\text{'}}_2=3\mu C$