The magnitude of work done in placing four charges at the corners of a square of side 'a' as shown in the figure, will be -

Options

A. `(4 - sqrt(2)) (Kq^2)/(a)`
B. `(4 + sqrt(2)) (Kq^2)/2`
C. `(4 - sqrt(2)) (Kq^2)/(a^2)`
D. `(4 + sqrt(2)) (Kq^2)/(a^2)`

Answer

A

Explanation

`4 ((k(q) (-q))/(a)) + 2(k(q)(q))/(asqrt(2))`

`W_("ext") = U_("sys") = 2 `
(`U_("one")` charge)(because system is symmetic)
`= 2 [(2k(q) (-q))/(a) + (kq^2)/(asqrt(2))]`
`= (2 kq^2)/(a) [(1 - 2sqrt(2))/(sqrt2)]`
`= (kq^2)/a [sqrt(2) - 4]`
`|W_("ext")| = (kq^2)/2 (4 - sqrt(2))`