Question

Two equally charged identical metal spheres $A$ and $B$ repel each other with a force $3 \times 10^{-5} N$. Another identical uncharged sphere $C$ is touched with $A$ and then placed at the midpoint between $A$ and $B$. Net force on $C$ is

• A. $1 \times 10^{-5} N$
• B. $2 \times 10^{-5} N$
• C. $1.5 \times 10^{-5} N$
• D. $3 \times 10^{-5} N$

Answer 1

Answer: (D)

Let $q$ be the charge on each metal spheres $A$ and $B$ respectively and $r$ is distance between them, then
$F=\frac{q \times q}{4 \pi \varepsilon_{0} r^{2}}=3 \times 10^{-5} N \dots$(i)
After contact, charge on $C=$ charge on $A=\frac{q}{2}$
Net force on $C=F_{B C}-F_{A C}$
$=\frac{q(q / 2)}{4 \pi \varepsilon_{0}(r / 2)^{2}}-\frac{(q / 2)(q / 2)}{4 \pi \varepsilon_{0}(r / 2)^{2}}$
$=\frac{q^{2}}{4 \pi \varepsilon_{0} r^{2}}=3 \times 10^{-5} N$ ( Using ( i ))