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The PE of an electric dipole in an external

U=-

where

I was under the impression I could find U, and then easily determine the force on the dipole using

F

F

F

however my book annoyingly states that these should be

F

F

F

which they give a derivation for in a different way. However they do go on to prove later that F

**E**-field isU=-

**p.E**where

**p**is it's dipole moment.I was under the impression I could find U, and then easily determine the force on the dipole using

**F=-∇U**, to obtainF

_{x}=p_{x}∂E_{x}/∂x+p_{y}∂E_{y}/∂x+p_{z}∂E_{z}/∂xF

_{y}=p_{x}∂E_{x}/∂y+p_{y}∂E_{y}/∂y+p_{z}∂E_{z}/∂yF

_{z}=p_{x}∂E_{x}/∂z+p_{y}∂E_{y}/∂z+p_{z}∂E_{z}/∂zhowever my book annoyingly states that these should be

F

_{x}=p_{x}∂E_{x}/∂x+p_{y}∂E_{x}/∂y+p_{z}∂E_{x}/∂zF

_{y}=p_{x}∂E_{y}/∂x+p_{y}∂E_{y}/∂y+p_{z}∂E_{y}/∂zF

_{z}=p_{x}∂E_{z}/∂x+p_{y}∂E_{z}/∂y+p_{z}∂E_{z}/∂zwhich they give a derivation for in a different way. However they do go on to prove later that F

_{L}=-∂U/∂L with L the direction in question. I'm now very confused. What is wrong with my approach?
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