Question

An electric dipole of dipole moment `vecP` is placed in a uniform electric field `vecE` with its axis inclined to the field. Write an expression for the torque `vecT` experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that the torque acting on it is:

1. maximum
2. Zero

An electric dipole of dipole moment `(vecp)` is kept in a uniform electric field `vecE`. Show graphically the variation of torque acting on the dipole (τ) with its orientation (θ) in the field. Find the orientation in which torque is (i) zero and (ii) maximum.

Answer 1

The torque experienced by the dipole is written as `vecT = vecP xx vecE`
(i) The torque experienced by a dipole is maximum when it is placed perpendicular to the direction of electric field as shown.

(ii) T= 0 if the dipole moments are parallel to the direction of electric field.

Answer 2

Graphical representation of the variation of torque acting on the dipole (τ) with its orientation (θ) in the field.

the orientation in which torque is (i) zero and (ii) maximum is:

Given, dipole moment = `vecP`

Electric field = `vecE`

Torque = `vecp xx vecE`

Torque depends upon the orientation of the dipole, as,

`|vectau|` = pE sinθ

(i) If θ = 0°

sin0° = 0

τ = 0 (minimum or zero)

(ii) If θ = 90°

sin90° = 1

|τ| = pE (maximum)