Calculate the work required to be done to make an arrangement of three particles each having a charge `+q` such that the particles lie at the vertices of an equilateral triagnle of side a. What work will be doen by electric field when the particles are shifted away so that the side of triangle becomes 2a ?

Explanation

The work required to make an arrangement of charges is equal to potential energy of the system
therefore` W = (q^(2))/(4 pi epsilon_(0)a) xx 3 = (3q^(2))/(4 pi epsilon_(0)a)`
work done by electric field represents the decrease in potential energy. so, we have
`W_("E.Field") = - Delta U = U_(i) - U_(f)`
Now, `U_(i) = (q^(2))/(4 pi epsilon_(0)(a)) xx 3 `
`U_(f) = (q^(2))/(4 pi epsilon_(0)(2a)) xx 3 `
`therefore " " W_("E.Field") = (3q^(2))/(4 pi epsilon_(0)a) - (3q^(2))/(8 pi epsilon_(0)a) = (3q^(2))/(8 pi epsilon_(0)a)`