A sperical ballon od radius R charged uniformly on its surface with surface density `sigma`. Find work done against electric forces in expanding it upto radius 2R.

Answer

`(-pi sigma^(2)R^(3))/in_(0)`

Explanation

`(U_("self"))_("Initial")=1/(4pi in_(0))(Q^(2)/(2R))`
`(U_("self"))_("final")=1/(4pi in_(0))(Q^(2)/(4R))`
Workdone against electric forces `=DeltaU`
`=-1/(4pi in_(0))Q^(2)/(4R)=-(pi sigma^(2)R^(3))/in_(0)`