COMEDK · Physics · 17. Electrostatics

Two identical conducting balls having unequal positive charges \(q_1\) and \(q_2\) are separated by a distance \(r\). If they are made to touch each other and then separated to the same distance, the force between them will be

A zero
B More than before
C Same as before
D Less than before

Verified Solution

Answer & Solution

Correct Answer

(B) More than before

Step-by-step Solution

Detailed explanation

Initial force: \(F_1 = k\dfrac{q_1 q_2}{r^2}\) After touching, each ball gets charge \(q' = \dfrac{q_1+q_2}{2}\) New force: \(F_2 = k\dfrac{\left(\dfrac{q_1+q_2}{2}\right)^2}{r^2}\) Comparing: since \(q_1 \neq q_2\), \((q_1-q_2)^2 > 0\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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