Eight point charges are placed at the comers of a cube of edge a as show in figure If the work done in disassembing this system of charges is `x (q^(2))/(4 pi epsi_(0) )` . Find x upto 2 decimal places.

Answer

5.82

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 charge are at a separation 12 like charges are at separation `sqrt(2)` a and 4 unlike charge are at separation `sqrt(2)` Therefore, the potential energy of the system is given as .
`U = (1)/(4 pi espi_(0)) [ (12) (l) (-1))/(a) + ((12) (q) (q))/(sqrt(2)a) + ((4)(q)(-q))/(sqrt(3)a)] = - 5.82 ((1)/(4 pi epsi_(0) . (q^(2))/(a))`
The binding energy of this system is therefore,
`|u| = 5.824 ((1)/(4 pi epsi_(0)) (q^(2))/(a))`.
So, work done by external forces in disassembling, this system of charges is
`w = 5.824 ((1)/(4 pi epsi_(0)).(q^(2))/(a))`