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),

Question

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 $K = \frac{1}{4 π ε _{0}}$ , the difference between the potential energies of configuration (2) and (1) is given by :

TestHub · Accepted Answer

​ u ⊕ ​ = ( 2 a K q 0 ​ ​ + 2 ​ a K q 0 ​ ​ ) q 0 ​ × 2 u 0 ​ = ( 2 a K q 0 ​ 2 ​ ​ + a K q 0 ​ ​ ) q 0 ​ × 2 ​ ​ So, Δ u = u 2 ​ − u 1 ​ = 2 q 0 ​ a k q 0 ​ ​ [ 2 2 ​ + 1 − 2 − 2 ​ 1 ​ ] ⇒ Δ u = 4 π ε 0 ​ a 2 q 0 2 ​ ​ [ 2 ​ 4 − 2 ​ − 1 ​ ] = 4 π ε 0 ​ a 2 q 0 2 ​ ​ 2 ​ ( 3 − 2 ​ ) ​ ⇒ Δ u = a 2 k q 0 2 ​ ​ [ 2 ​ 3 − 2 ​ ​ ] = a k q 0 2 ​ ​ ( 3 2 ​ − 2 ) ​

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