# derive an expression for the total work done in rotating an electric dipole through an angle theta in a uniform electric field.

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Potential Energy of an Electric Dipole, When Placed in a Uniform Electric Field

Supposean electric dipole of dipole momentpis placed along a direction, making an angleθwith the direction of an external uniform electric fieldE. Then, the torque acting on the dipole is given by

If the dipole is rotated through an infinitesimally small angledθ, against the torque acting on it, then the small work done is given by

If the dipole is oriented, making an angleθ1toθ2with the electric filed, then the total work done is given by

W=pE(cosθ1 cosθ2)

This work done is stored in the dipole in the form of its potential energy.

∴U=pE(cos 90 cosθ)

U= pEcosθ

U=

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