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Charges +q, -q, +q and -q are kept respectively at the four vertices of a square. The length of each side of the square is d. How much work should be done to bring a charge q to the centre of the square?

Asked in GSEB Board July 2023 · Work done in moving a charge

• (1) Zero
• (2) -(2√2 q²)/(4πε₀ d)
• (3) -((4-√2) q²)/(4πε₀ d)
• (4) (4√2 q²)/(4πε₀ d)

Step-by-step solution

Why the other options are wrong

• (2) Each -q is d/(√2) from the centre and contributes -(√2 q²)/(4πε₀ d) to the work; counting only these two gives this option. The two +q charges, at the same distance, cancel it exactly.
• (3) This is the work needed to assemble the four corner charges themselves: four adjacent pairs give -(4q²)/(4πε₀ d) and two diagonal pairs give +(2q²)/(4πε₀√2 d), a total of -((4-√2) q²)/(4πε₀ d). The question asks only for the extra work to bring q to the centre.
• (4) This adds the four contributions as magnitudes, ignoring their signs: 4×(√2 q²)/(4πε₀ d) = (4√2 q²)/(4πε₀ d). Potential is a signed sum, and the +q and -q terms cancel.

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