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

Explanation

We know the torfque on an electric dipole placed in an electric field , ` t = pEsintheta `
By definition work done by torque on the dipole
` dW = tdtheta `
` dW = pEsintheta .d theta `
Net work done to move from ` theta_(1) " to" theta_(2)` is given by
` W = int dW = int_(theta_(1))^(theta_(2)) p E sin theta d theta `
` W = -pE ( cos theta)_(theta_(2))^(theta_(1))`
` W = -pE ( cos theta_(2) - cos theta_(1))`
Taking ` theta_(1) = 90^(@) and theta_(2) = theta ` we can write .
` W = - pE cos theta `
` W = barp. vecE`
This work done will be stored in the form of potential energy.
` i.e, P.E = - vecp. vecE`