Electric Dipole

To find the change in potential energy of the dipole when it is rotated in an electric field, we use the formula for the potential energy of a dipole in an electric field:

where:

• is the dipole moment,
• is the electric field strength,
• is the angle between the dipole moment and the electric field.

Initially, the dipole is aligned with the electric field, so the initial angle . The potential energy is:

After rotation by , the new angle , and the potential energy becomes:

The change in potential energy is given by:

Substitute the expressions for and :

Given , the expression becomes:

Substitute and :

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