derive an expression for potential energy of an electric dipole in a uniform electric field .

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

Suppose an electric dipole of dipole moment *p *is placed along a direction, making an angle *θ*with the direction of an external uniform electric field *E*. Then, the torque acting on the dipole is given by

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

If the dipole is oriented, making an angle *θ*_{1} to *θ*_{2} with the electric filed, then the total work done is given by

*W* = *pE* (cos *θ*_{1} − cos *θ*_{2})

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

∴*U* = *pE* (cos 90° − cos *θ*)

*U* = − *pE* cos *θ*

*U* = −

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