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Q3.An electric dipole is held in uniform electric field I.Using suitable diagram show that,it doesn't undergo translatory motion and derive an expression for the torque acting on it and specify its direction.

Let us consider an electric dipole placed in a uniform electric field  in a region of space (shown by 'parallel' lines of force in figure.
The dipole moment vector  making an angle ? with the field . Let -q and +q be the charges forming the dipole and 2l the distance between them. Due to the electric field , the charge +q experiences a force q  (in the direction of the field) and the charge -q experiences an equal and opposite force q  (opposite to the field). Since the two forces are equal and opposite, the net translatory force on the dipole in 'uniform' electric field is zero; therefore there will be to translatory motion of the dipole in a uniform electric field. 
However, the forces q , q act at different points and form a couple which tens to set the dipole parallel to the field . The moment of this restoring couple is known as the 'torque'  on the dipole. The magnitude of the torque (= force × perpendicular distance) is given by 
     = qE (2l sin?) = 2ql E sin ? 
or  = pE sin ? newton - metre, 
where p(= 2ql) is the magnitude of the dipole moment. 
In vector form: 
Thus, in a uniform electric field, a dipole feels a torque (but no net force). In the torque is perpendicular to the page, pointing downwards (right-hand screw rule)
If the dipole be placed perpendicular to the elelectric field (? = 90o or sin ? = 1), then the torque acting on it will be maximum. If this be  then, 
or 
If E = 1 newton/coulomb, then   coulomb-metre. Hence, the moment of an electric dipole is the torque acting on the dipole placed perpendicular to the direction of a uniform electric field of intensity 1 newton/coulomb. 



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