An electric dipole of dipole moment $p$ is aligned parallel to a uniform electric field $E$. The energy required to rotate the dipole by $ 90^\circ $ is :

Question

A charge of 2 $\mu C$ is placed in an electric field of intensity $ 4 \times 10^3 \, \text{N/C} $. What is the force experienced by the charge?

Answer 1

To determine the energy required to rotate an electric dipole in a uniform electric field, we need to understand the concept of potential energy for an electric dipole. The potential energy $ U $ of a dipole with dipole moment $ \mathbf{p} $ that makes an angle $ \theta $ with a uniform electric field $ \mathbf{E} $ is given by the formula:

U = -\mathbf{p} \cdot \mathbf{E} = -pE \cos \theta

Initially, the dipole is aligned parallel to the electric field, which means the angle $ \theta $ is $ 0^\circ $. Therefore, the initial potential energy $ U_i $ is:

U_i = -pE \cos 0^\circ = -pE

When the dipole is rotated by $ 90^\circ $, the angle $ \theta $ becomes $ 90^\circ $. The potential energy $ U_f $ at this position is:

U_f = -pE \cos 90^\circ = 0

The work done or the energy required to rotate the dipole from its initial position to the final position is the change in potential energy, given by:

\Delta U = U_f - U_i = 0 - (-pE) = pE

Thus, the energy required to rotate the dipole by $ 90^\circ $ is pE, which matches the correct answer.

Hence, the correct answer is:

pE

Answer 2