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 the field is changed by an angle 60. 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)

-3 J

Dipole moment of each molecule $={10}^{-30}Cm$

$1$ mole of the substance contains $6\times {10}^{23}$ molecules,

Total dipole moment of all the molecules, $p=6\times {10}^{23}\times {10}^{-30}=6\times {10}^{-7}Cm$

$E={10}^7$

Initial potential energy, $U_i=-pEcos\theta =-6\times {10}^{-7}\times {10}^{7}cos{0}^o=-6J$

Final potential energy, $U_f=-6\times {10}^{-7}\times {10}^7\times cos{30}^o=-3J$

Work done= $-\left(\text{Change in Potential energy}\right)=-\left[\right(-3)-(-6\left)\right]=-3J$

So, correct option is $\left(C\right)$