A molecule of a substance has a permanent electric dipole moment of magnitude `10^-29C` m. A mole of this substance is polarised ( at low temperature )by applying a strong electrostatic field of magnitude `10^6Vm^-1`. The direction of the field is suddenly changed by an angle of `60^@`. Estimate the heat released by the substance in aligning its dipoles along the new direcation of the field. For simplicity. assume `100%` polarisation of the sample .

Explanation

Here, dipole moment of each molecules
`= 10^(-29) C m`
As 1 mole of the substance contains
`6 xx 10^(23)` molecules,
total dipole moment of all the molecules,,
`p = 6 xx 10^(23) xx 10^(-29) cm`
`= 6 xx 10^(-6) cm`
Initial potential energy, `U_(t) = - pE cos theta`
`= - 6 xx 10^(-6) xx 10^(6) cos 0^(@) = - 6 J`
Fina potential energy (when `theta = 60^(@)`),

`U_(f) = - 6 xx 10^(-6) xx 10^(6) xx cos 60^(@) = - 3J`
Change in potential energy
`= - 3 J - (- 6 hat(j)) = 3 J`
So, there is loss in potential energy. This must be the energy released by the substace in the form of heat in aligning its dipoles.