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. $-6 \, J$
• B. $-3 \, J$
• C. $3 \, J$
• D. $6 \, J$

Answer 1

Answer: (B)

Dipole moment of each molecules $= 10^{-30} \,C m$.
As $1$ mole of the substance contains $6 \times 10^{23}$ molecules
Total dipole moment of all the molecules
$p = 6 \times 10^{23}\times10^{-30}\,C m = 6 \times10^{-7} \,C m$
Initial potential energy, $U_{i}=-pEcos\theta $
$=-6\times10^{-7}\times10^{7}\,cos\,0^{\circ}$
$=-6\,J$
Final potential energy, $U_{f} =-6\times10^{-6}\times10^{6}\times cos\,60^{\circ}$
$=-3\,J$
Work done = -[Change in potential energy]
$=-\left[\left(-3\right)-\left(-6\right)\right]=-3\,J$