Derive an expression for the total work done in rotating the electric dipole through an angle theta in a uniform electric field.
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Analogous to the work
W=FΔs
done by a force F over a distance Δs , there is also a work done by a torque T for a rotational movement
W=TΔθ
where Δθ is the angle of rotation. The torque experienced by an electric dipole with dipole moment p⃗ in an electric field E⃗ is
T⃗ =p⃗ ×E⃗ =pEsinθ
were θ is the angle between the dipole moment and the electric field. Thus the work performed during a rotation of a dipole from an angle θ=α to an angle θ=β is given by
W=∫βαT(θ)dθ=∫βαpEdθsinθ
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