Question

An electric dipole has the magnitude of its charge as $q$ and its dipole moment is $p$. It is placed in a uniform electric field $E$. If its dipole moment is along the direction of the field, the force on it and its potential energy is respectively
(A) $q, E$, and max
(B) $2q, E$ and min
(C) $q, E$, and min
(D) Zero and min

Answer 1

Hint: Two equal and opposite charges separated by a distance is called a dipole. The product of one of the two charges and the distance between them is called the dipole moment. We have the magnitude of charge and the dipole moment given. We have to find the field, force, and potential energy if the dipole moment is along the direction of the field.

Complete Step by step solution,
When a dipole is placed in an electric field. Let $\theta $ be the angle between the electric field and the dipole moment. The charges will experience a force. The forces acting on the charges will also be equal in magnitude and opposite in direction. Thus the two equal and opposite forces separated by a distance will contribute a couple.
The magnitude of the moment acting on the couple is also called torque.
Torque is given by
$T = pE\sin \theta $
Where $T$ stands for the torque, $p$ stands for the dipole moment, $E$ stands for the electric field, and $\theta $ is the angle between the dipole moment and the electric field.
 Here, it is given that the dipole moment is along the direction of the electric field.
Hence the angle between the dipole moment and the electric field $\theta = 0$
We know that, $\sin 0 = 0$
Then the torque will be,
$T = pE\sin 0 = pE \times 0 = 0$
The potential energy can be written as,
$U = - pE\cos \theta $
We know that the angle $\theta = 0$
$\cos 0 = 1$
Therefore, the potential energy will be,
$U = - pE\cos 0 = - pE \times 1 = - pE$
This means that the potential energy is minimum.
Therefore,

The answer is Option (D) Zero and min.

Note:
For molecules like $C{O_2}$,$C{H_4}$etc. the centers of positive charges and negative charges will coincide. Hence they will not have a dipole moment. Such molecules are called non-polar molecules. When an electric field is applied, it will develop a dipole moment. In molecules like water, the centers of positive and negative charges do not coincide. Hence they have a permanent electric dipole and are called polar molecules.