An electric dipole of dipole moment P⃗ is placed parallel to the uniform electric field of intensity E⃗. On rotating it through angle of 90° from this situation, the amount of work done is .

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(2) PE. Given: the dipole starts parallel to E⃗, so θ₁=0°, and is turned to θ₂=90°. Idea: the field exerts a torque τ=PE sin θ that opposes the turning, so the work done is W=∫_θ₁^θ₂PE sin θ dθ=PE(cos θ₁-cos θ₂). W=PE(cos 0°-cos 90°)=PE(1-0) W=PE Read as energy: U=-PE cos θ rises from -PE at the parallel position to 0 at 90°, an increase of PE, which is exactly the work supplied.

An electric dipole of dipole moment P⃗ is placed parallel to the uniform electric field of intensity E⃗. On rotating it through angle of 90° from this situation, the amount of work done is ________.

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