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Question

Answer the following Questions.
Find expressions for the force and torque on an electric dipole kept in a uniform electric field.

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Solution

Let an electric dipole be rotated in electric field from angle θ0 and θ1 in the direction of electric field. In this process the angle of orientation θ is changing continuously; hence the torque also changes continuously. Let at any time, the angle between dipole moment p and electric field E be θ then
Torque on dipole τ=pEsinθ
The work done in rotating the dipole a further by small angle dθ is
dW=Torque×angular displacement=pEsinθdθ
Total work done in rotating the dipole from angle θ0 to θ1 is given by
W=θ1θ0pEsinθdθ=pE[cosθ]θ1θ0
=pE[cosθ1θ0]=pE(cosθ0cosθ1)....(i)
Special case : If electric dipole is initially in a stable equilibrium position (θ0=0) and rotated through an angle θ(θ1=θ) then work done
W=pE[cos0cosθ]=pE(1cosθ)....(ii).

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