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In the first configuration (1) shown in the figure, four identical charges q₀ are kept at the corners A, B, C and D of a square of side a. In the second configuration (2), the same charges are shifted to the midpoints G, E, H and F of the sides of the square [so that G, E, H and F form a square of side a/(√2)]. If K=1/(4πε₀), the difference between the potential energies of configuration (2) and configuration (1) is

Asked in JEE Main 24th Jan 2nd Shift 2025 · Energy of a system of charges

• (1) (Kq₀²)/a(4√2-2)
• (2) (Kq₀²)/a(3-√2)
• (3) (Kq₀²)/a(3√2-2)
• (4) (Kq₀²)/a(4-2√2)

Step-by-step solution

Why the other options are wrong

• (1) Subtracts only the four side pairs of configuration (1), leaving its two diagonal pairs out, so 4√2+2-4 survives.
• (2) The key with the √2 moved from the 3 to the 2; no counting of pairs gives it, since swapping side and diagonal distances in configuration (2) gives √2 and in configuration (1) gives 2√2.
• (4) Not reachable by one slip: counting only the side pairs in each configuration gives 4√2-4 and counting only the diagonal pairs gives 2-√2, neither of which is 4-2√2.

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