Charges `+q` and `-q` are located at the corners of a cube of side as show in the figure. Find the work done to separate the charges to infinite distance

Answer

`W=5.824[q/(4pi in_(0) a)]`

Explanation

For potential energy of the system of charges total number of charge pairs will be `.^(8)C_(2)` or `28` of these `28` pairs 12 unlike charges are at a separation a, `12` like charges are at a `sqrt(2)` a and `4` unlike charges are at separation `sqrt(3)a`. Therefore, the potential energy of the system.
`U = (1)/(4pi epsilon_(0)) [((12)(q)(-q))/(a)+((12)(q)(q))/(sqrt(2)a)+((4)(q)(-q))/(sqrt(3)a)]`
`= - 5.824 ((1)/(4pi epsilon_(0)).(q^(2))/(a))`
The binding energy of this system is therefore,
`|U| = 5.824((1)/(4pi epsilon_(0))(q^(2))/(a))`
So, work done by external forces in diassembling, this system of charges is
`W = 5.824 ((1)/(4 pi epsilon_(0)).(q^(2))/(a))`