Question: Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct?
Step 1 (Governing Principles): [0.25 Mark]
When two charged conductors are brought into contact, charge flows from the conductor at a higher potential to the one at a lower potential until both attain a common potential ($V$). The total charge of the system is conserved according to the law of conservation of charge.
Step 2 (Mathematical Derivation): [0.5 Mark]
- Total charge of the system: $Q_{total} = q_1 + q_2$
- Total capacitance of the system (in parallel): $C_{total} = C_1 + C_2 = 4\pi\varepsilon_0 r_1 + 4\pi\varepsilon_0 r_2 = 4\pi\varepsilon_0(r_1 + r_2)$
- The common potential $V$ is given by: $$V = \frac{Q_{total}}{C_{total}} = \frac{q_1 + q_2}{4\pi\varepsilon_0(r_1 + r_2)}$$
Step 3 (Analysis and Conclusion): [0.25 Mark]
- (A) Correct: Charge is conserved.
- (B) Correct: Spheres attain a common potential.
- (C) Correct: Matches the derived formula $V = \frac{1}{4\pi\varepsilon_0} \frac{(q_1 + q_2)}{(r_1 + r_2)}$.
- (D) Incorrect: This expression does not represent the common potential of the system.
Final Answer: The statement that is not correct is (D).
💡 EL10 Concept Insight: Think of charge like water in two connected tanks; water flows until the levels (potential) are the same, and the total amount of water (charge) stays the same, but the final level depends on the total capacity (sum of radii) of the tanks combined.