Question

how do we derive the formula for electric potential for an electric dipole along axial position?

Answer 1

Let, +q and –q are the charges along the line               
                                                                                                     
Q Potential at a point, which is at a distance r from the center,

           1              q
 V = -- ------- X -------                                                                                                                       4 πε0          r     
                              1              q
So, here Vq    = ------- X ----------                                  
                             4 πε0    (a + r)                              

             1              -q         
V-q    = ------- X ----------                          
           4 πε0         (r-a)   

Now,  V = Vq + V-q        
                                      q            2a 
 So,       Potential   = -------  X  ----------                          
                                  4 πε0      (a2-r2)  
 

Answer 2

Explanation:

V=4πε01((r2−4a2)4a)

V=4πε01((r2−4a2)2P)

Hence, the electric potential is 4πε01((r2−4a2)2P