Q.Define electric dipole and find an expression for the electric potential at a point on the axis of an electric dipole.

An electric dipole's axial potential is found by superposing the potentials of its two point charges; for points far from the dipole, this simplifies neatly to V = kp/r^2, decaying faster than a single point charge's 1/r potential.

Electric dipole: A system consisting of two equal and opposite point charges, +q and -q, separated by a small distance 2a. Its strength is characterized by the electric dipole moment p = q (2a), a vector directed from the negative to the positive charge.

Potential at an axial point:

Let the dipole have charges -q at point A and +q at point B, separated by 2a, with the dipole centre at O. Consider a point P on the axis (the line through A and B extended), at distance r from the centre O, on the side of the +q charge.

Distance from P to +q charge: (r - a)

Distance from P to -q charge: (r + a)

Total potential at P (potential is a scalar, so contributions simply add):

V = k [ q/(r-a) - q/(r+a) ]

= k q [ (r+a) - (r-a) ] / [ (r-a)(r+a) ]

= k q (2a) / (r^2 - a^2)

Since p = q(2a):

V = k p / (r^2 - a^2)

Short dipole approximation (r >> a):

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