Derive an expression for potential energy of electric - di-pole placed in a n uniform electric field .

Explanation

We know that torque on an electric dipole placed in an electric field, `tau=pE sin theta`
By definition work done by torque on the dipole
`dW=tau d theta`
i.e., `dW=pEsin theta .d theta`
Net work done to move from `theta_1` to `theta_2` is given
by `W=int dW=int_(theta_1)^(theta_2) pE sin theta d theta`
i.e., `W=-pE (cos theta )_(theta_1)^(theta_2)`
i.e., `W=-pE (cos theta_2 - cos theta_1)`
Taking `theta_1=90^@` and `theta_2=theta` , we can write ,
`W=-pE cos theta `
or `W=-vecp.vecE` .
This work done will be stored in the form of potential energy .
i.e., `P.E.=-vecp.vecE`