An electric dipole with dipole moment 5 × 10^–6 Cm is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is:

The correct option is 1.0 J.

Understanding the Potential Energy of a Dipole:
The potential energy ($U$) of an electric dipole with dipole moment ($p$) placed in a uniform electric field ($E$) is given by the formula:
$U=-pEcos\theta$
where $\theta$ is the angle between the electric dipole moment vector and the direction of the electric field vector.

Step-by-Step Calculation:
1. Identify the given parameters:
Dipole moment,
$p=5\times {10}^{-6}\text{ C m}$
Uniform electric field,
$E=4\times {10}^5\text{ N/C}$

2. Determine initial and final orientations:
Initially, the dipole is aligned in the direction of the electric field:
${\theta }_1=0^{\circ }$
Finally, the dipole is rotated to an angle of 60° with respect to the field:
${\theta }_2={60}^{\circ }$

3. Formulate the change in potential energy ($\Delta U$):
The change in potential energy is the difference between the final potential energy and the initial potential energy:
$\Delta U=U_2-U_1$
$\Delta U=-pEcos{\theta }_2-(-pEcos{\theta }_1)$
$\Delta U=pE(cos{\theta }_1-cos{\theta }_2)$

4. Substitute the values:
Using $cos{0}^{\circ }=1$ and $cos{60}^{\circ }=0.5$:
$\Delta U=(5\times {10}^{-6})\times (4\times {10}^5)\times (1-0.5)$
$\Delta U=2.0\times 0.5$
$\Delta U=1.0\text{ J}$

Thus, the change in the potential energy of the dipole is 1.0 J.