Derive the equation for the couple acting on a electric dipole in a uniform electric field.

Explanation

(1) A pair of opposite charges separated by a small distance is called dipole.
(2) Consider the charge of dipole are -q and +q coulomb and the distance between them is 2a.
(3) Then the electric dipole moment P is given by `p=qxx2a=2aq`. It is a vector. Its direction is form -q to +q along the axis of dipole.
(4) It is placed in a uniform electric field E, making an angle `theta` with field direction as shown in fig.
(5) Due to electric field force on +q is `F =+qE` and force on -q is `F=-qE`.
(6) These two equal and opposite charge consitute torque or moment of couple.
i.e., torque, `tau = bot^(r)` distance `xx` magnitude of one of force
`:. tau=(2a sin theta)qE=2aqE sin theta=PE sin theta`
In vector form, `vec(tau)=vec(P)xxvec(E)`