deduce an expression for the electric potential due to an electric dipole at any point on the axis. mention any contrasting feature of electric dipole at a point as compared to that due to single charge

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$T a k e a d i p o l e o f l e n g t h 2 a w i t h c h a r g e + a n d - q t h e p o t e t i a l a t a p o i n t p o n a x i s w h i c h i s r d i s \tan c e f r o m c e n t e r o f t h e d i p o l e . V_{+ q} = \frac{k q}{r - a}; V_{- q} = \frac{- k q}{r + a} V_{n e t} = \frac{k q}{r - a} + \frac{- k q}{r + a} = \frac{2 q k a}{r^{2} - a^{2}} c o n t r a s t i n g f e a t u r e o f e l e c t r i c p o t e n t i a l o f a d i p o l e a t a p o i n t a s c o m p a r e d t o . . . d i p o l e p o t e n t i a l f a l l s o f f a s 1 / r 2 w h e r e a s t h e p o t e n t i a l d u e t o a \sin g l e c h a r g e f a l l s o f f a s 1 / r . R e g a r d s$

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