The work done in rotating an electric dipole in the electric field is
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Therefore we have that the work done by the external field in rotating the electric dipole through some angle is W=∫θfθiqEsinθrdθ+∫θfθiqEsinθrdθ. Therefore W=2∫θfθiqrEsinθdθ. where the electric dipole is given by →p=q→ℓ and has magnitude p=qℓ.
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