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 $60^{\circ }$. 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)

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, $U_i=-pEcos\theta$
$=-6\times 10^{-7}\times 10^{7}cos{0}^{\circ }$
$=-6J$
Final potential energy, $U_f=-6\times 10^{-6}\times 10^6\times cos60^{\circ }$
$=-3J$
Work done = -[Change in potential energy]
$=-\left[\left(-3\right)-\left(-6\right)\right]=-3J$