In the first configuration (1) as shown in the figure, four identical charges q₀ are kept at the corners A, B,…

Question

Two square configurations of four identical charges q0. In configuration 1 charges are at corners A, B, C, D of a square with midpoints G, E, H, F and center O. In configuration 2 charges are at midpoints G, E, H, F of the same square.

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:

A
$\frac{Kq_0^2}{a} (4\sqrt{2} - 2)$
B
$\frac{Kq_0^2}{a} (4 - \sqrt{2})$
C
$\frac{Kq_0^2}{a} (3\sqrt{2} - 2)$
D
$\frac{Kq_0^2}{a} (3 - \sqrt{2})$

Accepted Answer

C. $$\frac{Kq_0^2}{a} (3\sqrt{2} - 2)$$

Answer

A. $$\frac{Kq_0^2}{a} (4\sqrt{2} - 2)$$

Answer

B. $$\frac{Kq_0^2}{a} (4 - \sqrt{2})$$

Answer

D. $$\frac{Kq_0^2}{a} (3 - \sqrt{2})$$

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