A cube of edge `a` is placed at some distance from a long plane sheet of charge having surface density `sigma`. Find the electric energy stored in the cube.

Explanation

Electric field due to plane sheet `E = (sigma)/(2 in_(0))`
Energy density `u = (1)/(2) in_(0) E^(2)`
Energy stored in cube
`U = uV = (1)/(2) in_(0) E^(2) a^(3)`
`= (1)/(2) in_(0) ((sigma)/(2 in_(0)))^(2) a^(3)`
`= (sigma^(2) a^(3))/(8 in_(0))`