Two isolated conducting spheres S1 and S2 of radius 23R and 13R have 12 μC and − 3 μC 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 S1 and S2 are respectively:

# Two isolated conducting spheres S1 and S2 of radius $\frac{2}{3}\mathrm{R}$ and $\frac{1}{3}\mathrm{R}$ have $12\text{\hspace{0.17em}}\mathrm{\mu C}$ and $-\text{\hspace{0.17em}}3\text{\hspace{0.17em}}\mathrm{\mu C}$ 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 S1 and S2 are respectively:

1. A

$6\text{\hspace{0.17em}}\mathrm{\mu C}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}}\mathrm{\mu C}$

2. B

$+\text{\hspace{0.17em}}4.5\text{\hspace{0.17em}}\mathrm{\mu C}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}}4.5\text{\hspace{0.17em}}\mathrm{\mu C}$

3. C

$3\text{\hspace{0.17em}}\mathrm{\mu C}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}\hspace{0.17em}}6\text{\hspace{0.17em}}\mathrm{\mu C}$

4. D

$4.5\text{\hspace{0.17em}}\mathrm{\mu C}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{on}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{both}$

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### Solution:

Now ${\mathrm{Q}}_{1}+{\mathrm{Q}}_{2}={\mathrm{Q}}_{1}^{\mathrm{\prime }}+{\mathrm{Q}}_{2}^{\mathrm{\prime }}=12\mathrm{\mu C}-3\mathrm{\mu C}=9\mathrm{\mu C}$
$\begin{array}{l}\mathrm{&}{\mathrm{V}}_{1}={\mathrm{V}}_{2}⇒\frac{{\mathrm{KQ}}_{1}^{\mathrm{\prime }}}{\frac{2\mathrm{R}}{3}}=\frac{{\mathrm{KQ}}_{2}^{\mathrm{\prime }}}{\frac{\mathrm{R}}{3}}\\ {\mathrm{Q}}_{1}^{\mathrm{\prime }}=2{\mathrm{Q}}_{2}^{\mathrm{\prime }}⇒2{\mathrm{Q}}_{2}^{\mathrm{\prime }}+{\mathrm{Q}}_{2}^{\mathrm{\prime }}=9\mathrm{\mu C}\\ ⇒{\mathrm{Q}}_{2}^{\mathrm{\prime }}=3\mathrm{\mu C}\\ \mathrm{&}{\mathrm{Q}}_{1}^{\mathrm{\prime }}=6\mathrm{\mu C}\end{array}$  Register to Get Free Mock Test and Study Material

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