An electric dipole is a pair of equal and opposite charges a small distance apart. Its dipole moment p = q × 2a points from − to +. In a uniform field it feels no net force, but a torque τ = pE sin θ.
An electric dipole is a pair of charges +q and −q, equal in size and opposite in sign, separated by a small distance 2a. Its total charge is zero.
Dipoles occur in many places. In a water molecule, the oxygen atom attracts the shared electrons more strongly than the hydrogen atoms do. The oxygen side carries a small negative charge and the hydrogen side a small positive charge, so the molecule is a dipole. A dipole antenna is a rod in which charge moves back and forth, forming a dipole whose moment oscillates.
A dipole is described by its dipole moment, p, a vector:
p = q × 2a
Its direction is along the line joining the charges, from −q to +q. Its SI unit is the coulomb metre (C m).
Far from the dipole, compared with 2a, its field depends on q and 2a only through their product p. Two dipoles with the same p produce the same field at large distances. That is why p is used to describe a dipole.
Two dipoles have the same charges, but one has its charges twice as far apart. How do their dipole moments compare?
p = q × 2a. With q the same and the separation doubled, p doubles.
The fields of +q and −q nearly cancel at a distant point, because the two charges are almost the same distance away. A larger separation makes the cancellation less complete, so the field far away is stronger. It is proportional to p.
Place the dipole in a uniform external field E, the same size and direction everywhere.
The force on +q is qE, along the field. The force on −q is qE, against the field. The two forces are equal and opposite, so the net force is zero, and the centre of the dipole does not accelerate.
The two forces act at different points, the two ends of the dipole. If the dipole is at an angle θ to the field, the forces do not act along the same line. They form a couple and produce a torque:
τ = p E sin θ
The torque rotates p towards the direction of E. A compass needle in a magnetic field behaves in the same way.
Zero net force, non-zero torque. The field exerts equal and opposite forces on the two charges. Because they act at different points, they rotate the dipole towards the direction of the field.
A dipole in a uniform field points along the field (θ = 0°). Is there a torque? What if it is turned to θ = 90°?
At θ = 0°, sin θ = 0, so τ = 0. The two forces act along the axis of the dipole, on the same line, so they produce no rotation. If the dipole is turned slightly away, the torque turns it back. This is a stable position.
At θ = 90°, sin θ = 1, so τ = pE, the largest possible value. The forces are as far from acting along the same line as they can be.
At θ = 180°, sin θ = 0 again and τ = 0. But a small turn now produces a torque that turns the dipole further away. This position is unstable.
1An electric dipole consists of…
2The dipole moment p points…
3The size of the dipole moment is…
4Two dipoles have equal charges, but one has twice the separation. Its dipole moment is…
5A dipole in a uniform external field experiences…
6The torque on a dipole in a uniform field is maximum when the angle between p and E is…
Next: Gauss’s law, which relates the flux through a closed surface to the charge inside it.
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