Question

A molecule with dipole moment $p$ is placed in an electric field of strength $E$. Initially the dipole is aligned parallel to the field . If the dipole is to be rotated to be anti-parallel to the field , the work required to be done by an external agency is

• A. $-2pE$
• B. $-2pE$
• C. $pE$
• D. $2pE$

Answer 1

The correct option is D $2pE$

Let the dipole moment be $p$ and the external electric field strength be $E$.

From the data given in the question,

Initially, the dipole is along the direction of electric field

$\therefore$ Initial Potential energy of dipole $U_i=-pE\cos {\theta }_i$

$\Rightarrow U_i=-pE\cos 0^{\circ }=-pE$

Now, the dipole is rotated and kept in a direction anti-parallel to the direction of electric field.

In this situation, Potential energy of dipole is given by

$U_f=-pE\cos {\theta }_f$

$\Rightarrow U_f=-pE\cos {180}^{\circ }=+pE$

We know that, Workdone in rotating the electric dipole $W=U_f-U_i$

$\therefore W=pE-(-pE)=2pE$

Hence, option (d) is the correct answer.