COMEDK · Physics · 17. Electrostatics

Two point charges \(+8 \times 10^{-18}\) and \(+2 \times 10^{-18} C\) are fixed 10 cm apart. Where should we place a third charge \(10^{-7} \mathrm{C}\), so that it is in equilibrium?

A 6.67 m from the charge \(+2 \times 10^{-18} \mathrm{C}\)
B 6.67 cm from the charge \(+2 \times 10^{-18} \mathrm{C}\)
C 6.67 cm from the charge \(+8 \times 10^{-18} C\)
D 6.67 m from the charge \(+8 \times 10^{-18} \mathrm{C}\)

Verified Solution

Answer & Solution

Correct Answer

(C) 6.67 cm from the charge \(+8 \times 10^{-18} C\)

Step-by-step Solution

Detailed explanation

Since both charges are positive, the third charge must lie between them. Let \(x\) be the distance of the third charge from \(q_1 = +8 \times 10^{-18}\) C, so its distance from \(q_2 = +2 \times 10^{-18}\) C is \((10 - x)\) cm. For equilibrium, forces from both charges must be…

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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