Question

A molecule of a substance has a permanent electric dipole moment of magnitude ${10}^{-30}cm$. A mole of this substance is polarised by applying a strong electrostatic field of magnitude ${10}^{7}V{m}^{-1}$. The direction of field is changed by an angle ${60}^o$. The heat released by the substance in aligning its dipole along the new direction of the field is

• A. $-6J$
• B. $-3J$
• C. $3J$
• D. $6J$

Answer 1

Answer: (B)

$-3J$

Dipole moment of each molecules $={10}^{-30}cm$.
As $1$ mole of the substance contains $6\times {10}^{23}$ molecules
Total dipole moment of all the molecules
$p=6\times {10}^{23}\times {10}^{-30}Cm=6\times {10}^{-7}Cm$
Initial potential energy $U_i=-pE\cos \theta =-6\times {10}^{-7}\times {10}^7\cos 0^o=-6J$
Final potential energy $U_f=-6\times {10}^{-6}\times {10}^6\times \cos {60}^o=-3J$
Work done $=-$ (Change in potential energy)
$=-\left[\right(-3)-(-6\left)\right]=-3J$