Obtain an expression for the potential energy of a dipole in an external field.

Question: Obtain an expression for the potential energy of a dipole in an external field.

The potential energy of a dipole in an external field can be expressed as:

U = -p * E

where U is the potential energy, p is the electric dipole moment, and E is the external electric field. The negative sign indicates that the potential energy decreases as the dipole aligns with the field (lower potential energy corresponds to a more stable configuration). This expression can be derived from the work done by the external field in rotating the dipole from an initial orientation to a final orientation, taking into account the orientation-dependent torque exerted on the dipole by the field.

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