Deduce an expression for electric potential due to an electric dipole at any point on its axis. Mention one contrasting feature of electric potential of dipole at a point as compared to that due to a single charge.

Explanation

Consider a dipole is placed in the electric field E. Let `theta=` Angle made by the dipole with the electric field.

Torque acting on the dipole is given as
`tau=PEsintheta`
whose P = dipole moment of electric dipole
Let Work done. to rotate the dipole through angle `theta`.
`:.dW=taud theta`
Work done in rotating the dipole from `90^(@)` to `theta`
`W=int_(90^(@))^(theta)(PEsintheta)d theta=PEint_(90^(@))^(theta)sinthetad theta`
`W=PE|-costheta|_(90^(@))^(0)`
`W=PE|-costheta+0|`
`W=-PEcostheta`
This work done is stored in the electric dipole in the form of electric potential energy (U).
`impliesU=-PEcostheta`
In vector form
`U=-vecP.vecE`