Derive the formula for the electric potential due to an electric dipole at a far distant point from it.
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Let P be an axial point at distance r from the centre of the dipole.
Electric potential at point P will be
V = V1+V2 = -1/4Πɛ0
q/(r+a)+ 1/4Πɛ0
q/ (r-a) = q/4Πɛ0 [1/(r-a) - ( r+a)]
q/4Πɛ0 = 2a/(r^2 - a^2)
[q*2a = p]
For a far away point,
r>>a
Therefore, V = 1/4Πɛ0
p/r^2
At large distances, dipole potential falls off as 1/r², whereas the potential due to a single charge falls off as 1/r.
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