Three points charges of `1 C, 2C and 3C` are placed at the corners of an equilateral triangle of side 100 cm. Find the work done to move these charges to the corners of a similar equilateral triangle of side 50 cm.

Answer

`9.9xx10^(10) J`

Explanation

Here `q_(1) = 1C, q_(2) = 2C and q_(3) = 3C`.
`r_(1) = 100 cm = 1m`, Fig

Initial P.E. of system,
`U_(1) = (1)/(4pi in_(0) r_(1)) [q_(1) q_(2) + q_(2) q_(3) + q_(3) q_(1)]`
`= (9xx10^(9))/(1) [1 (2) + 2 (3) + 3 (1)] = 99xx10^(9) J`
when `r_(2) = 50cm = 0.5m`
final P.E. of system,
`U_(2) = (1)/(4pi in_(0) r_(2)) [q_(1) q_(2) + q_(2) q_(3) + q_(3) q_(1)]`
`= (9xx10^(9))/(0.5) [1 (2) + 2 (3) + 3 (1)]`
`= 2xx99xx10^(9) J`
work done = `U_(2) - U_(1) = 2xx99xx10^(9) - 99xx10^(9)`
`W = 99xx10^(9) J = 9.9xx10^(10) J`