In the first configuration (1) as shown in the figure, four identical… | JEE Main 2025 (24 Jan, Shift 2)

Q27JEE Main 2025 · 24 JAN · SHIFT 2Medium

Electrostatic Potential Energy

In the first configuration (1) as shown in the figure, four identical charges $(q_0)$ are kept at the corners A, B, C and D of square of side length ' $a$ '. In the second configuration (2), the same charges are shifted to mid points $G, E, H$ and $F$ , of the square. If $K = \frac{1}{4\pi\epsilon_0}$ , the difference between the potential energies of configuration (2) and (1) is given by:

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Answer: (d)

Config (1): 4 sides of length $a$ and 2 diagonals $\sqrt{2}a$ : $U_1 = \frac{Kq_0^2}{a}\left(4 + \frac{2}{\sqrt{2}}\right) = \frac{Kq_0^2}{a}(4 + \sqrt{2})$
Mid-points form a square of side $\frac{a}{\sqrt{2}}$ with diagonal $a$ .
Config (2): $U_2 = Kq_0^2\left(\frac{4\sqrt{2}}{a} + \frac{2}{a}\right) = \frac{Kq_0^2}{a}(4\sqrt{2} + 2)$
$U_2 - U_1 = \frac{Kq_0^2}{a}(3\sqrt{2} - 2)$ , answer (d).

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Electrostatic Potential Energy question from JEE Main 2025 (24 Jan, Shift 2)

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