COMEDK · Physics · 17. Electrostatics

PQRS is square of side \(1 \mathrm{~m}\). A charge of \(100 \mu \mathrm{C}\) is placed at the centre of the square. Then the work done to take \(3 \mu \mathrm{C}\) charge from the corner \(\mathrm{P}\) to the corner \(\mathrm{R}\).

A \(4.5 \times 10^5 \mathrm{~J}\)
B \(9 \sqrt{2} \times 10^5 \mathrm{~J}\)
C Zero
D \(1.8 \times 10^5 \mathrm{~J}\)

Verified Solution

Answer & Solution

Correct Answer

(C) Zero

Step-by-step Solution

Detailed explanation

The electric potential \(V\) at any point at a distance \(r\) from a point charge \(q\) is given by \(V = \dfrac{kq}{r}\). Let the charge at the centre of the square be \(Q = 100 \mu \text{C} = 100 \times 10^{-6} \text{C}\). The distance from the centre of a square of side…

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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