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 are respectively:

Answer 1

Hint: A dipole moment consists of oppositely charged particles placed a certain distance apart. The dipole moment is defined as the direction of the lining joining the negative and the positive charge.
Formula used: In this solution, we will use the following formula:
Force on a charge in an electric field $F = qE$ where $q$ is the charge of the dipole individual charges and $E$ is the electric field

Complete step by step answer:
When a dipole is placed in an external electric field, it will tend to align itself with the direction of the electric field. We’ve been told that the dipole moment is along the direction of the electric field.
Then the force acting on the positive charge due to the electric field will be $F = + qE$ and similarly the force on the negative charge due to the electric field will be $F = - qE$. Thus the net force on the dipole will be zero.
Not the potential energy of the dipole is the dot product of the dipole moment vector and the electric field. Since the dipole moment is along the direction of the field, the angle will be $\theta = 0^\circ $. Hence the potential energy will be
$U = - p.E = - pE\cos 0^\circ $
Which gives us
$U = - pE$
Which is the potential energy of the dipole.

Note: The potential energy of the dipole ranges from $U = - pE\,{\text{to}}\,U = pE$ for $\theta = 0^\circ \,{\text{to}}\,\theta = 180^\circ $. The force on the dipole in an external field will always be zero since the force on the two charges cancel each other out however the torque can be non-zero depending on the orientation of the dipole.