electric potential due to an electric dipole at any general point | class 12 | advguruji

Consider, an electric dipole of length 2a having charges +q and -q. A point P is at a distance r from the centre of the dipole such that OP is making an angle θ with dipole moment p.

CONSTRUCTION :-

Extend OP to BP such that BC is perpendicular to BP, Draw AD perpendicular to BP.

PROOF :-

Now, β = r + aCosθ     .........(1)

         α = r + aCosθ      .........(2)

Let, 'V1' and 'V2' be the potential due to +q and -q respectively.

Net electric potential at 'P' is -

              V = V1 + V2

            V = kq/α + k(-q)/β

            From equation (1) and (2)

          

Also,       p = q.2a

Therefore,

              [  V = kpCosθ/(r² - a²Cos²θ)   ]

Note :- For axial line, θ = 0

          For equatorial line, θ = π/2

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