Lesson 8 of 13 · 7 min
Electric dipole
NCERT §1.10
Tara holds the charged comb near a thin stream of water from the tap, and the stream bends towards it. Water is neutral. Why does it care?
The lesson in notes
In short
An electric dipole is two charges +q and −q, equal in size, held a distance 2a apart. Its dipole moment is p = q × 2a, a vector pointing from −q to +q. The SI unit is C m.
Its total charge is zero, but its field is not: the fields of +q and −q do not cancel exactly, and far away the dipole field falls off as 1/r³, faster than the 1/r² of a single charge.
On the axis at distance r from the centre: E = 2kp/r³ (r >> a), directed along p. The exact expression is E = k·4qar/(r² − a²)².
On the equatorial plane at distance r: E = kp/r³ (r >> a), directed opposite to p. The exact expression is E = k·2qa/(r² + a²)^(3/2).
At the same large distance, the axial field is twice the equatorial field.
Far fields depend on q and a only through the product p. A point dipole is the limit 2a → 0 with p kept finite; for it the 1/r³ formulas are exact.
Polar molecules such as H₂O have a permanent dipole moment because their centres of positive and negative charge do not coincide; CO₂ and CH₄ have zero dipole moment but acquire an induced one in an applied field.