Question

The distance between the centres of two identical solid spheres each of radius 5 cm kept in free space is 40 cm. If each one is holding a charge of $2,\mu C$, then the work done in bringing their centres to a separation of 30 cm is

• A. $36\times10^{-2}$ J
• B. $12\times10^{-2}$ J
• C. $6\times10^{-2}$ J
• D. $18\times10^{-2}$ J
• E. $3\times10^{-2}$ J

Hint:

Physics Tip: For like charges, bringing them closer always needs positive external work because repulsion increases potential energy.

Answer 1

Answer: (E)

Concept:
Work required to bring two like charges closer equals increase in electrostatic potential energy: $$W=\Delta U = kq_1q_2\left(\frac{1}{r_2}-\frac{1}{r_1}\right)$$
Step 1: Write given values.
Each sphere charge: $$q_1=q_2=2\mu C=2\times10^{-6}C$$ Initial separation: $$r_1=40\text{ cm}=0.4\text{ m}$$ Final separation: $$r_2=30\text{ cm}=0.3\text{ m}$$
Step 2: Apply formula.
$$W=9\times10^9(2\times10^{-6})^2\left(\frac{1}{0.3}-\frac{1}{0.4}\right)$$ $$=9\times10^9 \times 4\times10^{-12}\left(\frac{10}{3}-\frac{5}{2}\right)$$ $$=36\times10^{-3}\left(\frac{20-15}{6}\right)$$ $$=36\times10^{-3}\times\frac{5}{6}$$ $$=30\times10^{-3}$$ $$=3\times10^{-2}\text{ J}$$
Step 3: Match option.
Hence correct answer is Option (E). :contentReference[oaicite:2]{index=2}