How to calculate the potential enery of electric dipole?
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It's a matter of choice. You can set the potential energy to be any value at any angle. You don't even have to have a zero-value at all; you could make UUpurely positive or purely negative if you're feeling adventurous.
But the advantage for U(π/2)=0U(π/2)=0 is, as you said, the simple expression U(θ)=−pEcosθ=−p⃗ ⋅E⃗ U(θ)=−pEcosθ=−p→⋅E→ instead of U(θ)=−p⃗ ⋅E⃗ +UoU(θ)=−p→⋅E→+Uo. There's a nice notational similarity when you contrast this with the torque τ⃗ =p⃗ ×E⃗
But the advantage for U(π/2)=0U(π/2)=0 is, as you said, the simple expression U(θ)=−pEcosθ=−p⃗ ⋅E⃗ U(θ)=−pEcosθ=−p→⋅E→ instead of U(θ)=−p⃗ ⋅E⃗ +UoU(θ)=−p→⋅E→+Uo. There's a nice notational similarity when you contrast this with the torque τ⃗ =p⃗ ×E⃗
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