Define electric dipole moment Derive an expression for total work done in rotating the dipole through an angle in a uniform electric field.

Dipole moment (P) is a measure of the strength of electric dipole. It is a vector quantity whose magnitude is equal to product of the magnitude of either charge and the distance between them.

Expression of total work done
 
Potential energy  of dipole is the energy possessed by the dipole by virtue of its particular position in the electric field.
Suppose an electric dipole of moment P is oriented at an angle θ with the direction of uniform external electric field E
we know, the torque τ acting on the dipole is
                                                                   τ=pE sinθ
It tries to rotate the dipole .
Small amount of work done in rotating the dipole through a small angle dθ against the torque is  
                                                                                                                                                 dW=τdθ      =pE sinθdθ
Total work done in rotating the dipole from orientation θ1 to θ2 is

                                                         W=θ1θ2pE sinθdθ    =pE-cosθθ1θ2W=-pEcosθ2-cosθ1

 

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