# Potential energy of an electric dipole in electric field

## Homework Statement

Show that the energy of an ideal dipole p in an electric field E is given by

U = -p ⋅ E

## Homework Equations

Work = θτ where τ is torque

τ = p × E

## The Attempt at a Solution

U = ∫(p × E) dθ' (from θ to 0, since the dipole will eventually align itself with the magnetic field.)
=∫pE(sinθ')dθ'
=-pE(cosθ') with limits θ to 0
=-pE + pE(cosθ)
=p ⋅ E - pE

That's not what I needed to prove. Help?

## Answers and Replies

ehild
Homework Helper
The formula for the potential energy depends where the zero of the PE is placed. The potential energy is the work done by the force when the object moves from the initial position to the position of zero potential. If the potential energy of the dipole is zero when it is perpendicular to the electric field, you have to integrate from θ to pi/2.

• Sleepycoaster
The formula for the potential energy depends where the zero of the PE is placed. The potential energy is the work done by the force when the object moves from the initial position to the position of zero potential. If the potential energy of the dipole is zero when it is perpendicular to the electric field, you have to integrate from θ to pi/2.
Okay, thanks!