Lesson 2 of 13 · 7 min
Potential due to a dipole
NCERT §2.4
Meera's teacher hands her a plastic stick with two small beads 2 cm apart, one at +10 nC and one at −10 nC: a dipole you can hold. Where around it is the potential positive, where negative, and where zero?
The lesson in notes
In short
A dipole is charges +q and −q a distance 2a apart; its dipole moment p = q × 2a points from −q to +q.
Far from the dipole (r ≫ a), V = p cos θ/(4πε₀r²), where θ is the angle between p and the line to the point. In vector form V = p·r̂/(4πε₀r²).
On the axis (θ = 0° or 180°) V = ±p/(4πε₀r²); on the equatorial plane (θ = 90°) V = 0 everywhere.
Dipole potential falls as 1/r², faster than a single charge's 1/r, because the two opposite charges nearly cancel at a distance.
The dipole potential depends on direction as well as distance: it is not spherically symmetric, unlike a point charge's.
Zero potential on the equatorial plane does not mean zero field there: E on the equator is p/(4πε₀r³), pointing opposite to p.