Electric dipole

An electric dipole is a pair of equal and opposite charges, +q and –q, a small distance 2a apart. Many molecules, such as water, behave like dipoles.

Its strength is the dipole moment: p = q × 2a. It is a vector pointing from –q to +q. Unit: C m.

Example: ±2 µC, 3 mm apart: p = 2 × 10⁻⁶ × 3 × 10⁻³ = 6 × 10⁻⁹ C m.

The total charge is zero, but the field is not, because the two charges are at different places. Far away (r much larger than a):

• On the axis (the line through both charges): E = 2kp / r³, in the same direction as p.
• On the equatorial line (the perpendicular bisector): E = kp / r³, opposite to p.

So at the same distance, the axial field is twice the equatorial field. Both fall as 1/r³, faster than a single charge's 1/r², because the two opposite charges nearly cancel from far away.

A dipole in a uniform field: +q is pushed one way and –q the other with equal forces, so the net force is zero. But the two forces act at different points, so they turn the dipole. The torque is:

τ = pE sin θ, where θ is the angle between p and E.

• θ = 0: no torque, and the dipole is in stable equilibrium (lined up with E).
• θ = 90°: maximum torque, pE.
• θ = 180°: no torque again, but unstable: a small push turns it all the way round.

In a non-uniform field, the dipole also feels a net force. This is why a charged comb attracts neutral bits of paper: it induces tiny dipoles in them, in a field that is stronger near the comb.