The electric energy stored in a cube

Options

A. `(sigma^(2)a^(3))/(8 epsilon_(0))`
B. `(sigma^(2)a^(3))/(4 epsilon_(0))`
C. `(sigma^(2)a^(3))/(2 epsilon_(0))`
D. `(sigma^(2)a^(3))/(epsilon_(0))`

Answer

1

Explanation

The energy density `u` i.e. energy stored per unit volume in an electric field `E` is
`u = (1)/(2) in_(0) E^(2)`
Electric field due to plate `E = (sigma)/(2 in_(0))`
Volume of cube `= a^(3)`
Electrical energy stored in the cube
`U = u xx "volume" = (1)/(2) in_(0) E^(2) xx a^(3)`
`= (1)/(2) in_(0) ((sigma)/(2 in_(0)))^(2) xx a^(3) = (sigma^(2) a^(3))/(8 in_(0))`