A cube of marble having each side 1 cm is kept in an electric field of intensity 300 V/m. Determine the energy contained in the cube of dielectric constant 8.
[Given : `epsilon_(0) =8.85 xx 10^(-12) C^(2)//Nm^(2)`]

Explanation

Data: `k=8, L=10^(-2)m, E=300 V//m`.
`epsilon_(0)=8.85 xx 10^(-12) C^(2)//N.m^(2)`
The energy density in the marble,
`u=1/2 epsilon_(0)kE^(2) =1/2(8.85 xx 10^(-12))(8)(300)^(2)`
`=3.186 xx 10^(-6) J//m^(3)`
`therefore` the energy contained in the marble cube
`=mu xx "volume" = u xx L^(3)`
`=(3.186 xx 10^(-6))(10^(-2)) = 3.186 xx 10^(-12)` J