how do we show that the net potential is 0 for an electric dipole along an equitorial dipole - Physics - Electrostatic Potential And Capacitance

Question

how do we show that the net potential is 0 for an electric
dipole along an equitorial dipole?

Jyoti Pant · Accepted Answer

From the figure above

At equatorial position lets say we take a point P . The distance of P from center O of dipole =r i.e as shown in figure OP=r

now AP=BP

$\sqrt{r^{2} + l^{2}} T h e e l e c t r i c p o t e n t i a l a t P d u e t o c h \arg e - q a t A V_{1} = \frac{1}{4 π \in_{0}} \frac{- q}{A P} = - \frac{1}{4 π \in_{0}} \frac{q}{\sqrt{r^{2} + l^{2}}} S a m e w a y e l e c t r i c p o t e n t i a l a t P d u e t o c h \arg e + q a t B V_{2} = \frac{1}{4 π \in_{0}} \frac{q}{B P} = \frac{1}{4 π \in_{0}} \frac{q}{\sqrt{r^{2} + l^{2}}} t h u s n e t p o t e n t i a l a t P V = V_{1} + V_{2} = - \frac{1}{4 π \in_{0}} \frac{q}{\sqrt{r^{2} + l^{2}}} + \frac{1}{4 π \in_{0}} \frac{q}{\sqrt{r^{2} + l^{2}}} = 0$

how do we show that the net potential is 0 for an electric dipole along an equitorial dipole?