Question

Obtain an expression for electric potential ‘V’ at a point in an end-on position i.e. axial position of the electric dipole. 

Answer 1

Electric potential at point P is the sum of electric potential due to the two charges – q and + q of the electric dipole, situated at A and B respectively as shown in the figure.
 `therefore V = V_(-q) + V_+q = - k q/((AP)) + k (q)/(BP)`

= `K_q (1/(BP) - 1/(AP)) - K_q (1/(r-a) - 1/(r+a))` 

= `k_q {((r+a) - (r-a))/(r^2 - a^2}} = K_q {(2a)/(r^2 - a^2}}`

⇒ `V = k.((q xx 2a))/(r^2 - a^2) = k.P/(r^2 - a^2)` (`p = q xx 2a` is the electric dipole moment)

As a << r (Since dipole has a very small size.)

So `r^2 - a^2 ≈ r^2`

`therefore V ≈ KP/r^2 = 1/(4pi∈_0).P/r^2`