Question

Two identical small conducting spheres, having charges of opposite sign, attract each other with a force of $0.108N$ when separated by $0.5m$. The spheres are connected by a conducting wire, which is then removed, and thereafter, they repel each other with a force of $0.036N$. The initial charges of the spheres are :

• A. $\pm 5\times {10}^{-6}Cand\mp 15\times {10}^{-6}C$
• B. $\pm 1.0\times {10}^{-6}Cand\mp 3.0\times {10}^{-6}C$
• C. $\pm 2.0\times {10}^{-6}Cand\mp 6.0\times {10}^{-6}C$
• D. $\pm 0.5\times {10}^{-6}Cand\mp 1.5\times {10}^{-6}C$

Answer 1

The correct option is B $\pm 1.0\times {10}^{-6}Cand\mp 3.0\times {10}^{-6}C$

Let initial charge be Q1 and Q2.
Initial force $=F=\frac{K\times Q1\times Q2}{r^2}=-0.108$
$F=\frac{9\times {10}^9\times Q1\times Q2}{0.25}=-0.108$

$Q1\cdot Q2=-3\times {10}^{-12}$

Now on connecting them, since they are identical so they will have equal charges.
Final charge $=\frac{Q1+Q2}{2}$

Final force $=F=\frac{9\times {10}^9\times (Q1+Q2{)}^2}{4\times 0.25}=0.036$
$Q1+Q2=\pm 2\times {10}^{-6}$

$Q2=\pm 1.0\times {10}^{-6}C,Q1=\mp 3.0\times {10}^{-6}C$