Derive an expression for torque experiencedby electric dipole in a uniform electric field

Explanation

Electric dipole : A pair of equal and opposite charges separated by certain distance is known as an electric dipole. Consider an electric dipole consisting of charges `- q and + q` placed in uniform electric field `vecE`.
Let 2a= Length of the dipole. and `theta `= angle made by electric dipole with the direction of electric field.

`vecF = - q vecE` = Force acting on charge - q at A.
`vecF_2 = +q vecE` = Force acting on charge + q at B.
Torque = Either force `xx` Perpendicular distance between the two forces.
`tau = qE (AN)`
`tau = qE (2 a sin theta)`
`tau = q (2a) E sin theta`
We know `q (2a) = P `= Dipole moment
`therefore tau = PE sin theta `
In vector form
`vec(tau) = vecP xx vecE` .