Lesson 9 of 13 · 11 min
Dipole in a uniform external field
NCERT §1.11
Put a dipole between two large charged plates, where the field is the same everywhere. It turns, but it does not slide towards either plate. Yet the comb pulls paper bodily. What is different?
The lesson in notes
In short
In a uniform field the forces qE and −qE on the two charges are equal and opposite, so the net force on a dipole is zero.
The two forces act at different points and form a couple: torque τ = p × E, of magnitude τ = pE sin θ, where θ is the angle between p and E.
The torque turns the dipole towards alignment with E. It is maximum (pE) at θ = 90° and zero when p is parallel or antiparallel to E.
In a non-uniform field there is also a net force. With p parallel to E the dipole is pulled towards the stronger field; with p antiparallel it is pushed towards the weaker field.
A comb run through dry hair attracts uncharged bits of paper: the comb's field polarises the paper, inducing a dipole along the field, and because the comb's field is non-uniform the paper is pulled towards the comb.